The ratio of the side lengths of a triangle is 10.5 : 18 : 22.5. The perimeter of the triangle is 408 centimeters. Determine whether the triangle is a right triangle.

Ok.

The "correct way to use the info to answer this problem is:

Add the "ratio sides" 10.5 + 18 + 22.5 = 51

then decide what the scaling factor is: 51 times what is 408? Or 408 divided by 51 is what.

Answer is 8

So multiply each side length by 8 and use Pythagorean's theorem

(remember that hypotenuse (c) is the longest side)

10.5 x 8 = 84 84^2 + 144^2 = 180^2

18 x 8 = 144. 7056 + 20736 = 32400

22.5 x 8 = 180 27792 = not equal. So it's not a rt. triangle

Realistically that used huge numbers that you don't have to ...

you could have just used Pythagorean's Theorem on the ratio sides

10.5^2 + 18^2 = 22.5^2

110.25 + 324 = 506.25

434.25 = nope still doesn't work