JIPMAT 2024 (QA) - The sides of four triangles are given below. Which of them forms a right triangle ? (A) 20 ~cm, 22 ~cm, 24 ~cm (B) 15 ~cm, 32 ~cm, 37 ~cm (C) 11 ~cm, 60 ~cm, 61 ~cm (D) 6 ~cm, 8 ~cm, 10 ~cm | PYQs + Solutions | AfterBoards
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JIPMAT 2024

Geometry
>
Triangles

Easy

The sides of four triangles are given below. Which of them forms a right triangle ?
(A) 20 cm,22 cm,24 cm20 \mathrm{~cm}, 22 \mathrm{~cm}, 24 \mathrm{~cm}
(B) 15 cm,32 cm,37 cm15 \mathrm{~cm}, 32 \mathrm{~cm}, 37 \mathrm{~cm}
(C) 11 cm,60 cm,61 cm11 \mathrm{~cm}, 60 \mathrm{~cm}, 61 \mathrm{~cm}
(D) 6 cm,8 cm,10 cm6 \mathrm{~cm}, 8 \mathrm{~cm}, 10 \mathrm{~cm}

Correct Option: 4
Check each triangle using the Pythagorean theorem (a2+b2=c2)(a^2 + b^2 = c^2).
For (A) 20 cm, 22 cm, 24 cm: \newline 202+222=400+484=88420^2 + 22^2 = 400 + 484 = 884
242=57624^2 = 576
884≠576884 \neq 576 → Not a right triangle \newline \hspace{5cm} \newline For (B) 15 cm, 32 cm, 37 cm: \newline 152+322=225+1024=124915^2 + 32^2 = 225 + 1024 = 1249
372=136937^2 = 1369
1249≠13691249 \neq 1369 → Not a right triangle \newline \hspace{5cm} \newline For (C) 11 cm, 60 cm, 61 cm: \newline 112+602=121+3600=372111^2 + 60^2 = 121 + 3600 = 3721
612=372161^2 = 3721
3721=37213721 = 3721 → This is a right triangle! \newline \hspace{5cm} \newline For (D) 6 cm, 8 cm, 10 cm: \newline 62+82=36+64=1006^2 + 8^2 = 36 + 64 = 100
102=10010^2 = 100
100=100100 = 100 → This is a right triangle! \newline \hspace{3cm} \newline Both triangles (C) and (D) satisfy the Pythagorean theorem.

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