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