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nevsk [136]
3 years ago
14

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

Mathematics
2 answers:
lana [24]3 years ago
5 0
2x^2=(3root2)^2
2x^2=9(2)
x^2=9
x= 3,-3

x=3 because your side length can’t be negative.
oee [108]3 years ago
3 0
<h3>Answer:  x = 3</h3>

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

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.

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