Question

Do the following side lengths form a right triangle?

14, 20, 15

Answer 1

no

Does a triangle with sides 14, 15 and 20 can form a right triangle?

To check if a triangle is a right one, we can follow these steps:

Step 1: Take the longest side as the candidate for the hypotenuse (c). Here, the longest side is that of lenght 20. So, c = 20. The other sides are leg A (a) and leg B (b). In this case we can assume that a = 14 and b = 15 .

Step 2: Now plug in these values in the formula below to check its validity:

c2 = a2 + b2

202 = 142 + 152

400 ≠ 421

As both sides of the above equation are not equal, we can surely say that the triangle [14 15 20] is NOT a right triangle.

Answer 2

Answer: No, the sides do not form a right triangle.

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Step-by-step explanation:

Let c = 20 be the largest or longest side. If we had a right triangle, then this side is the hypotenuse.

a = 14 and b = 15 are the other sides in either order.

Plug the values into the pythagorean theorem equation. Evaluate each side separately until getting a single numeric value.

`a^2 + b^2 = c^2\\\\14^2 + 15^2 = 20^2\\\\196 + 225 = 400\\\\421 = 400\\\\`

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

For more information, check out the pythagorean theorem converse.