Answers:
x = 14
y = 14
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Explanation:
The tickmarks indicate the sides x and y are the same length.
So y = x or x = y
We can use the Pythagorean theorem to say
a^2 + b^2 = c^2
x^2 + y^2 = (14*sqrt(2))^2
x^2 + x^2 = 14^2*(sqrt(2))^2
2x^2 = 196*2
x^2 = 196 ...... divide both sides by 2
x = sqrt(196)
x = 14
This must mean that y = 14 as well.
This triangle is an isosceles right triangle. We also consider it a 45-45-90 triangle because the three angles are 45, 45, and 90 degrees.
For any 45-45-90 triangle, the hypotenuse is always sqrt(2) times the leg length.
hypotenuse = leg*sqrt(2)