Question

Options are:

X=2, Y=3

X=3, Y=2

X= -2, Y=3

X=4, Y=8

Answer 1

x = 4, y = 8

Explanation:

If the triangles are congruent by the HL Theorem, it means that the hypotenuse and one leg of the right triangle are congruent to the corresponding one leg and hypotenuse of the other.

Thus;

2x - 5 = y - 5 (Eqn 1) and

y - 3 = x + 1 (Eqn 2)

Thus:

Rewrite equation 1

2x = y - 5 + 5

2x = y

Substitute y = 2x in equation 2.

y - 3 = x + 1 (Eqn 2)

2x - 3 = x + 1

Collect like terms

2x - x = 3 + 1

x = 4

Substitute x = 4 in equation 1

2x - 5 = y - 5 (eqn 1)

2(4) - 5 = y - 5

8 - 5 = y - 5

3 = y - 5

3 + 5 = y

8 = y

y = 8