Can sides 5 cm, 12 cm, and 13 cm form a right triangle?

Class 7The Triangle and its PropertiesTriangles

AYes, because $5^{2} + 1 2^{2} = 1 3^{2}$
BNo, because 5 + 12 is greater than 13
CNo, because the sides are all different
DIt cannot be told without measuring an angle

Step-by-Step Solution

Check:

5^{2} + 1 2^{2} = 25 + 144 = 169 = 1 3^{2}

. Since the sum of squares of the two shorter sides equals the square of the longest, it is a right triangle.

Answer: A) Yes, because

5^{2} + 1 2^{2} = 1 3^{2}

Key idea: Triangle inequality

**The sum of any two sides of a triangle is greater than the third side.**

So a triangle with sides 3, 4, 5 works (3+4>5, 3+5>4, 4+5>3). But sides 1, 2, 5 do NOT form a triangle — 1 + 2 = 3 is less than 5, so the two short sides can't reach across.

Use this to test whether three given lengths can be a triangle, or to bound a missing side: if two sides are 5 and 8, the third must be greater than 8 − 5 = 3 AND less than 8 + 5 = 13.

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