Question

Triangles S U V and R U W are connected at point U. Angles S U V and W U T are right angles. The length of hypotenuse S V is 2 x + 9 and the length of hypotenuse W T is 4 x minus 1. Sides V U and U W are congruent.

Which value of x would make Triangle S U V Is-congruent-to Triangle T U M by HL?

2
3
4
5

Answer 1

HL (Hypotenuse-Leg) requires the right triangles to have a congruent hypotenuse and a congruent leg. VU and UW are congruent legs, so set the hypotenuses equal:

2x + 9 = 4x − 1
10 = 2x ⇒ x = 5.

So x = 5.