Question

Given right triangle A w/a hypotenuse length of 3y + x and a leg of y-x, and right triangle B, w/ a hypotense length of y+5 and a leg length of x+5, for what values of x and y are the triangles congruent by HL?

Answer 1

Triangle A

hypotenuse: 3y + x
leg: y - x

Triangle B

hypotenuse: y + 5
leg: x + 5

Congruency => 3y + x = y + 5 and y - x = x + 5

Solve the system

3y + x = y + 5 -> 2y + x = 5
y - x = x + 5 -> y - 2x = 5

  2y + x = 5
-2y + 4x = -10

5x = -5
x = -1
y = (5 -(-1)) / 2 = 6/2 = 3

Verify:

 hypotenuses
3y + x = 9 - 1 = 8
y + 5 = 3 + 5 = 8

Legs:

y - x = 3 -(-1) = 3 + 1 = 4
x + 5 = -1 + 5 = 4.

Then both hypotenuses and both legs are congruent.

Answer: x = -1 and y = 3