Question

Does 2, 5, and 7 make a right triangle

Answer 1

Answer:  No, we don't have a right triangle

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Explanation:

If a triangle with sides a,b,c makes the equation a^2+b^2 = c^2 true, where c is the longest side, then this triangle is a right triangle. This is the converse of the pythagorean theorem.

Here we have a = 2, b = 5 and c = 7.

So...

a^2+b^2 = c^2

2^2+5^2 = 7^2

4+25 = 49

29 = 49

The last equation is false, so the first equation is false for those a,b,c values. Therefore, we do not have a right triangle.

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In contrast, consider the classic 3-4-5 right triangle

a = 3, b = 4 and c = 5 would make a^2+b^2 = c^2 true because 3^2+4^2 = 5^2 is a true equation (both sides lead to 25).