Question

- ne side of some triangles are given below. Find out which ones are right-angled triangles ? i) 8, 15, 17 ii) 11.60 61​

Answer 1

Answer:

i. 82 = 64, 152 = 225, 172 = 289 Now, 64 + 225 = 289 ∴ 82 + 152 = 172 The above expression is of the from (hypotenuse)2 = (base)2 + (height)2 ∴ The sides of lengths 8,15,17 will form a right-angled triangle. ii. 112 = 121, 122 = 144, 152 = 225 But, 121 + 144 ≠ 225 ∴ 112 + 122 ≠ 252 ∴ The above expression is not of the from (hypotenuse)2 = (base)2 + (height)2 ∴ The sides of lengths 11, 12, 15 will not form a right-angled triangle. iii. 112 = 121, 602 = 3600, 612 = 3721 Now, 121 + 3600 = 3721 ∴ 112 + 602 = 612 ∴ The above expression is of the from (hypotenuse)2 = (base)2 + (height)2 ∴ The sides of lengths 11, 60, 61 will form a right-angled triangle. iv. 1.52 = 2.25, 1.62 = 2.56, 1.72 = 2.89 But, 2.25 + 2.56 ≠ 2.89 ∴ 1.52 + 1.62 ≠ 1.72 ∴ The above expression is not of the from (hypotenuse)2 = (base)2 + (height)2 ∴ The sides of lengths 1.5, 1.6, 1.7 will not form a right-angled triangle v. 402 = 1600, 202 = 400, 302 = 900 But, 400 + 900 ≠ 1600 ∴ 202 + 302 ≠ 402 ∴ The above expression is not of the from (hypotenuse)2 = (base)2 + (height)2 ∴ The sides of lengths 40, 20, 30 will not form a right-angled triangle.Read more on Sarthaks.com - https://www.sarthaks.com/862135/the-sides-some-triangles-are-given-below-find-out-which-ones-are-rightangled-triangles-iii

Answer 2

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i. 82 = 64, 152  = 225, 172  = 289  Now, 64 + 225 = 289  ∴ 82 + 152  = 172   The above expression is of the from (hypotenuse)2  = (base)2  + (height)2   ∴ The sides of lengths 8,15,17 will form a right-angled triangle. ii. 112  = 121, 122  = 144, 152  = 225  But, 121 + 144 ≠ 225  ∴ 112  + 122  ≠ 252   ∴ The above expression is not of the from (hypotenuse)2  = (base)2  + (height)2   ∴ The sides of lengths 11, 12, 15 will not form a right-angled triangle. iii. 112  = 121, 602  = 3600, 612  = 3721  Now, 121 + 3600 = 3721  ∴ 112  + 602  = 612   ∴ The above expression is of the from (hypotenuse)2  = (base)2  + (height)2   ∴ The sides of lengths 11, 60, 61 will form a right-angled triangle. iv. 1.52  = 2.25, 1.62  = 2.56, 1.72  = 2.89  But, 2.25 + 2.56 ≠ 2.89  ∴ 1.52  + 1.62  ≠ 1.72   ∴ The above expression is not of the from (hypotenuse)2  = (base)2  + (height)2   ∴ The sides of lengths 1.5, 1.6, 1.7 will not form a right-angled triangle v. 402  = 1600, 202  = 400, 302  = 900 But, 400 + 900 ≠ 1600  ∴ 202  + 302  ≠ 402   ∴ The above expression is not of the from (hypotenuse)2  = (base)2  + (height)2   ∴ The sides of lengths 40, 20, 30 will not form a right-angled triangle.Read more on Sarthaks.com - https://www.sarthaks.com/862135/the-sides-some-triangles-are-given-below-find-out-which-ones-are-rightangled-triangles-iii