Question

Find the value of x. Write your answer in simplest form. WILL MAKE BRAINLIEST

Answer 1

2x^2=(3root2)^2
2x^2=9(2)
x^2=9
x= 3,-3

x=3 because your side length can’t be negative.

Answer 2

Answer:  x = 3

============================================

Explanation:

Since we have an isosceles right triangle, the the length of the hypotenuse (let's call it y) is equal to sqrt(2) times the leg length x.

In other words, $y = x*\sqrt{2}$

If we replaced y with 3*sqrt(2), then we could say,

$y = x*\sqrt{2}\\\\3\sqrt{2} = x*\sqrt{2}$

in which we can see that x = 3 must be the case. Or you could divide both sides of that last equation by sqrt(2) to find x = 3.

-------------------------

Another method:

We'll use the pythagorean theorem

$a^2+b^2 = c^2\\\\x^2+x^2 = \left(3\sqrt{2}\right)^2\\\\2x^2 = 3^2*\left(\sqrt{2}\right)^2\\\\2x^2 = 9*2\\\\2x^2 = 18\\\\x^2 = 18/2\\\\x^2 = 9\\\\x = \sqrt{9}\\\\x = 3$

We get the same answer as before.