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vovangra [49]
3 years ago
5

What is the value of x?

Mathematics
1 answer:
hoa [83]3 years ago
7 0
Because the two triangles together create another 90 degree angle on the right-most side, we can tell the triangle is a 45-45-90 triangle

So the base of the height (the given value is 3). Because it is a 45-45-90, the height is also 3. 

You can now find x by using Pythagorean theorem OR just the proof of a 45-45-90 triangle.

Pythagorean theorem version: 

a^2 + b^2 = c^2 
3^2 + 3^2 = x^2
9 + 9 = x^2
18 = x^2
x = 3\sqrt{2}

45-45-90 proof

The legs of a 45-45-90 triangle are congruent so you just take the value of a leg and place a \sqrt{2} at the end of it. 

Leg length is 3 units. Slap a \sqrt{2} on the end; answer is 3\sqrt{2}
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