Answer:
x = y = (15/2)√2
Explanation:
You can recognize this as an isosceles right triangle, so x=y. They Pythagorean theorem then tells you that ...
15² = x² + x²
225/2 = x²
√(225/2) = x = √(225·2/4) = (15/2)√2
The solution is x = y = (15/2)√2.
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Comment on isosceles right triangles
It is worth remembering that the ratio of sides of an isosceles right triangle is ... side : side : hypotenuse = 1 : 1 : √2.
Knowing this lets you write down the solution to this problem as ...
x = y = 15/√2
Of course, the denominator of this fraction can be rationalized by multiplying the fraction by (√2)/(√2) to get (15√2)/2 or (15/2)√2.