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Question

Which of the following lengths make a right triangle?

A
5,3,14
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B
6,23,8
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C
32,42,52
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D
23,22,25
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Solution

The correct options are
A 5,3,14
C 32,42,52
D 23,22,25
If in a triangle, the square of the longest side equals the sum of the squares of the other two sides, then the triangle is right-angled.

(5)2+32=5+9=14=(14)2

Thus, the lengths 5,3 and 14 form a right-triangle.

Similarly, (32)2+(42)2=18+32=50=(52)2
shows that the lengths 32,42 and 52 form the sides of a right-angled triangle.

Similarly, (23)2+(22)2=12+8=20=(25)2 shows that the lengths 23,22 and 25 form the sides of a right-angled triangle.

But, 62+(23)2=36+12=4864=82)

Thus, 6,23 and 8 would not form a right triangle.

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