{"id":68357,"date":"2021-03-19T10:47:14","date_gmt":"2021-03-19T05:17:14","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=68357"},"modified":"2022-04-01T10:28:00","modified_gmt":"2022-04-01T04:58:00","slug":"worksheet-on-pythagorean-theorem","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/worksheet-on-pythagorean-theorem\/","title":{"rendered":"Worksheet on Pythagorean Theorem | Pythagorean Theorem Worksheet with Answers"},"content":{"rendered":"<p>Worksheet on Pythagorean Theorem is helpful for the students who are willing to solve the problems based on the right-angled triangle, Pythagorean theorem. If you are preparing for any exam, then you can begin preparation by referring Pythagorean Theorem Worksheet. Make use of these Pythagoras Theorem Questions during practice and perform well in the test. We have covered various types of questions that use Pythagorean Statements. So, Practice all the questions from the worksheet as many times as possible so that you will understand the concept easily.<\/p>\n<h2>What is Pythagorean Theorem?<\/h2>\n<p>Pythagoras theorem states that &#8220;In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of other two sides&#8221;. The three sides of the right-angled triangle are the perpendicular side, base, and hypotenuse side, where the hypotenuse is the largest side. Pythagorean formula is hypotenuse\u00b2 = base\u00b2 +perpendicular_side\u00b2.<\/p>\n<p>c\u00b2 = a\u00b2 + b\u00b2<\/p>\n<p>Where a is base side<\/p>\n<p>b is perpendicular side<\/p>\n<p>c is hypotenuse side<\/p>\n<h3>How to Solve Problems on Pythagorean Theorem?<\/h3>\n<p>Check out the manual procedure in the below sections. Follow these guidelines to solve the Pythagorean theorem.<\/p>\n<ul>\n<li>Look at all terms in the question.<\/li>\n<li>Find out which vertex has the right angle.<\/li>\n<li>Start with those right triangles and apply the Pythagorean theorem.<\/li>\n<\/ul>\n<p><strong>Also, Read<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/ccssmathanswers.com\/word-problems-on-pythagorean-theorem\/\" target=\"_blank\" rel=\"noopener\">Word Problems on Pythagorean Theorem<\/a><\/li>\n<\/ul>\n<p><strong>Question 1: <\/strong><\/p>\n<p>In \u2206ABC right angled at A. If AB = 16 m and BC = 8 cm, then find the length of AC?<\/p>\n<details>\n<summary>Solution:<\/summary>\n<p>Given that,<\/p>\n<p>The sides of the right-angled triangle AB = 8 cm, BC = 10 cm<\/p>\n<p>As per the Pythagorean Theorem,<\/p>\n<p>hypotenuse\u00b2 = base\u00b2 +perpendicular_side\u00b2<\/p>\n<p>BC\u00b2 = AC\u00b2 + AB\u00b2<\/p>\n<p>AC\u00b2 = BC\u00b2 &#8211; AB\u00b2<\/p>\n<p>AC = \u221a(BC\u00b2 &#8211; AB\u00b2)<\/p>\n<p>Substitute AB, BC values in the above formula<\/p>\n<p>AC = \u221a(10\u00b2 &#8211; 8\u00b2)<\/p>\n<p>= \u221a(100 &#8211; 64)<\/p>\n<p>= \u221a(36)<\/p>\n<p>= 6<\/p>\n<p>Therefore AC = 6 cm.<\/p>\n<\/details>\n<hr \/>\n<p><strong>Question 2:<\/strong><\/p>\n<p>A ladder 7 m long when set against the wall of the house just reaches a window at a height of 24 m from the ground. How far is the lower end of the ladder from the base of the wall?<\/p>\n<details>\n<summary>Solution:<\/summary>\n<p>Let the ladder be AC = 7 m<\/p>\n<p>Let the vertical height reached be BC = 24 m<\/p>\n<p>Let the distance between the foot of the ladder and wall be AB = x meters<\/p>\n<p>By Pythagoras Theorem,<\/p>\n<p>AB\u00b2 = AC\u00b2 + BC\u00b2<\/p>\n<p>x\u00b2 = 7\u00b2 + 24\u00b2<\/p>\n<p>x\u00b2 = 49 + 576<\/p>\n<p>x\u00b2 = 625<\/p>\n<p>x = 25<\/p>\n<p>Therefore, the foot of the ladder is 25 m away from the wall.<\/p>\n<\/details>\n<hr \/>\n<p><strong>Question 3:<\/strong><\/p>\n<p>A carpet measures 7 feet long and has a diagonal measurement of 74 square feet. Find the width of the carpet.<\/p>\n<details>\n<summary>Solution:<\/summary>\n<p>Given that,<\/p>\n<p>Length of the carpet = 7 feet<\/p>\n<p>Diagonal of the carpet = 74 sq ft<\/p>\n<p>In a rectangle,<\/p>\n<p>diagonal\u00b2 = length\u00b2 + width\u00b2<\/p>\n<p>width\u00b2 = diagonal\u00b2 &#8211; length\u00b2<\/p>\n<p>= 74 &#8211; 7\u00b2<\/p>\n<p>= 74 &#8211; 49<\/p>\n<p>= 25<\/p>\n<p>width = \u221a(25)<\/p>\n<p>= 5 ft<\/p>\n<p>Therefore, the width of the carpet is 5 ft.<\/p>\n<\/details>\n<hr \/>\n<p><strong>Question 4:<\/strong><\/p>\n<p>Jim starts driving east for 9 miles, then takes a left turn, and then he drives north for another 40 miles. At the end of driving, what is the distance of a straight line from the starting point?<\/p>\n<details>\n<summary>Solution:<\/summary>\n<p>As given in the question,<\/p>\n<p>Driving for east = 9 miles<\/p>\n<p>Driving for north = 40 miles<\/p>\n<p>Let the straight line distance = x<\/p>\n<p>The equation will be<\/p>\n<p>a\u00b2 + b\u00b2 = c\u00b2<\/p>\n<p>9\u00b2 + 40\u00b2 = x\u00b2<\/p>\n<p>81 + 1600 = x\u00b2<\/p>\n<p>1681 = x\u00b2<\/p>\n<p>x = \u221a(1681)<\/p>\n<p>x = 41<\/p>\n<p>Therefore, the straight line distance from the starting point is 41 miles<\/p>\n<\/details>\n<hr \/>\n<p><strong>Question 5:<\/strong><\/p>\n<p>The base of an isosceles triangle is 24 cm and the two equal sides are 37 cm each. Find the altitude AD of the triangle.<\/p>\n<details>\n<summary>Solution:<\/summary>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-68919\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/03\/worksheet-on-pythagoras-theorem-1.png\" alt=\"Worksheet On Pythagorean Theorem 1\" width=\"335\" height=\"356\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/03\/worksheet-on-pythagoras-theorem-1.png 335w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/03\/worksheet-on-pythagoras-theorem-1-282x300.png 282w\" sizes=\"(max-width: 335px) 100vw, 335px\" \/><\/p>\n<p>Altitude AD divides the triangle ABC into two equal parts.<\/p>\n<p>By using the pythagorean theorem for \u25b3 ADC, \u25b3BCD<\/p>\n<p>hypotenuse\u00b2 = base\u00b2 + perpendicular_side\u00b2<\/p>\n<p>37\u00b2 = 12\u00b2 + x\u00b2<\/p>\n<p>1369 = 144 + x\u00b2<\/p>\n<p>1369 &#8211; 144 = x\u00b2<\/p>\n<p>x\u00b2 = 1225<\/p>\n<p>x = \u221a(1225)<\/p>\n<p>x = 35<\/p>\n<p>So, the length of the altitude is 35 cm.<\/p>\n<\/details>\n<hr \/>\n<p><strong>Question 6:<\/strong><\/p>\n<p>The length of a living room is 2 feet less than twice its width. If the diagonal is 2 feet more than twice the width, find the dimensions of the room?<\/p>\n<details>\n<summary>Solution:<\/summary>\n<p>Let the width of the living room = x<\/p>\n<p>Given that,<\/p>\n<p>Length of the living room = 2 feet less than twice its width<\/p>\n<p>= 2x &#8211; 2<\/p>\n<p>Diagonal = 2 feet more than twice the width<\/p>\n<p>= 2x + 2<br \/>\nFrom the given equations<\/p>\n<p>diagonal\u00b2 = length\u00b2 + width\u00b2<\/p>\n<p>(2x + 2)\u00b2 = (2x &#8211; 2)\u00b2 + x\u00b2<\/p>\n<p>4x\u00b2 + 8x + 4 = 4x\u00b2 &#8211; 8x + 4 + x\u00b2<\/p>\n<p>8x + 8x = 5x\u00b2 &#8211; 4x\u00b2 + 4 &#8211; 4<\/p>\n<p>16x = x\u00b2<\/p>\n<p>x = 16<\/p>\n<p>So, the width of the living room is 16 ft<\/p>\n<p>Length of the living room = 2(16) &#8211; 2 = 32 &#8211; 2 = 30 ft<\/p>\n<p>Diagonal of the living room = 2(16) + 2 = 32 + 2 = 34 ft<\/p>\n<\/details>\n<hr \/>\n<p><strong>Question 7:<\/strong><\/p>\n<p>A bird was sitting 9 feet from the base of an oak tree and flew 15 feet to reach the top of the tree. How tall is the tree?<\/p>\n<details>\n<summary>Solution:<\/summary>\n<p>The distance between bird sitting position and tree is 9 ft<\/p>\n<p>The bird flew 15 ft to reach top of the tree<\/p>\n<p>According to the Pythagorean theorem<\/p>\n<p>c\u00b2 = a\u00b2 + b\u00b2<\/p>\n<p>15\u00b2 = 9\u00b2 + b\u00b2<\/p>\n<p>225 = 81 + b\u00b2<\/p>\n<p>b\u00b2 = 225 &#8211; 81<\/p>\n<p>b\u00b2 = 144<\/p>\n<p>b = \u221a(144)<\/p>\n<p>b = 12<\/p>\n<p>Therefore, the height of the tree is 12 ft.<\/p>\n<\/details>\n<hr \/>\n<p><strong>Question 8:<\/strong><\/p>\n<p>Mary wants to cut across a rectangular lot rather than walk around it. Of the lot is 120 feet long and 50 feet wide. Mary walks diagonally across the lot, how many feet is the short cut?<\/p>\n<details>\n<summary>Solution:<\/summary>\n<p>Given that,<\/p>\n<p>Length of the lot = 120 ft<\/p>\n<p>Width of the lot = 50 ft<\/p>\n<p>Let the shortcut distance be x<\/p>\n<p>As per the Pythagorean theorem,<\/p>\n<p>a\u00b2 + b\u00b2 = c\u00b2<\/p>\n<p>50\u00b2 + 120\u00b2 = x\u00b2<\/p>\n<p>2500 + 14400 = x\u00b2<\/p>\n<p>16900 = x\u00b2<\/p>\n<p>x = \u221a(16900)<\/p>\n<p>x = 130<\/p>\n<p>Therefore, 130 ft is the shortcut.<\/p>\n<\/details>\n<hr \/>\n","protected":false},"excerpt":{"rendered":"<p>Worksheet on Pythagorean Theorem is helpful for the students who are willing to solve the problems based on the right-angled triangle, Pythagorean theorem. If you are preparing for any exam, then you can begin preparation by referring Pythagorean Theorem Worksheet. Make use of these Pythagoras Theorem Questions during practice and perform well in the test. &#8230; <a title=\"Worksheet on Pythagorean Theorem | Pythagorean Theorem Worksheet with Answers\" class=\"read-more\" href=\"https:\/\/bigideasmathanswers.com\/worksheet-on-pythagorean-theorem\/\" aria-label=\"More on Worksheet on Pythagorean Theorem | Pythagorean Theorem Worksheet with Answers\">Read more<\/a><\/p>\n","protected":false},"author":12,"featured_media":69868,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[5],"tags":[],"jetpack_featured_media_url":"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/03\/Worksheet-on-Pythagorean-Theorem.png","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/68357"}],"collection":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/users\/12"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=68357"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/68357\/revisions"}],"predecessor-version":[{"id":92287,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/68357\/revisions\/92287"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media\/69868"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=68357"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=68357"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=68357"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}