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The sides of four triangles are as follows. Which of them forms a right triangle ? (I) \(20 \mathrm{~cm}, 22 \mathrm{~cm}, 24 \mathrm{~cm}\) (II) \(15 \mathrm{~cm}, 32 \mathrm{~cm}, 37…

Question and options

The sides of four triangles are as follows. Which of them forms a right triangle ?

(I) 20 cm,22 cm,24 cm20 \mathrm{~cm}, 22 \mathrm{~cm}, 24 \mathrm{~cm}

(II) 15 cm,32 cm,37 cm15 \mathrm{~cm}, 32 \mathrm{~cm}, 37 \mathrm{~cm}

(III) 11 cm,60 cm,61 cm11 \mathrm{~cm}, 60 \mathrm{~cm}, 61 \mathrm{~cm}

(IV) 6 cm,8 cm,10 cm6 \mathrm{~cm}, 8 \mathrm{~cm}, 10 \mathrm{~cm}
  1. (I) and (II) only
  2. (II) and (III) only
  3. (IV) only
  4. (III) and (IV) only

Answer and explanation

Correct answer: D - (III) and (IV) only
Check whether the square of the longest side equals the sum of the squares of the other two. III: 11^2 + 60^2 = 121 + 3600 = 3721 = 61^2. IV: 36 + 64 = 100 = 10^2. I (884 against 576) and II (1249 against 1369) fail, so only III and IV are right triangles.

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