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

Set the hypotenuses equal because HL (right triangles) requires equal hypotenuse and a corresponding leg.
2x + 9 = 4x − 1
10 = 2x → x = 5.

(Check: 2·5+9 = 19 and 4·5−1 = 19, and VU = UW, so triangles are congruent by HL.)