Question

What is the value of x?

Answer 1

`\displaystyle 12 = x`

Explanation:

The Pythagorean Triple for this whole triangle is 15, 20, 25, according to this genuine pythagorean statement [from adding up the hypotenuse]:

`\displaystyle a^2 + b^2 = c^2 \\ \\ 20^2 + 15^2 = 25^2 \\ \\ 400 + 225 = 625`

`\displaystyle 625 = 625`☑

So now that we know we are right in the ballpark, we can solve for x, but this time, RQ is the hypotenuse:

`\displaystyle -16^2 + 20^2 = x^2 \\ \\ -256 + 400 = x^2 \\ \\ √(144) = √(x^2); 12 = x`

There is ONE MORE STEP we have to take before we are finished. We need to check to make sure that 9, 12, 15 is a pythagorean triple, with SR representing the hypotenuse:

`\displaystyle 9^2 + 12^2 = 15^2 \\ \\ 81 + 144 = 225`

`\displaystyle 225 = 225`☑

Therefore, 9, 12, 15 is a Pythagorean Triple.

I am joyous to assist you anytime.