Question

In triangle RTS △RTS shown below, point U is on

ST, and point V is on RT so that angle RST UVT∠RST≅∠UVT. If ST=13 VT=5, and RV=13.2, find the length of TU. Figures are not necessarily drawn to scale.

Answer 1

Answer: 7

Explanation:

As
`\angle T \cong \angle T` by the reflexive property, we know that
`\triangle RST \sim \triangle UVT` by AA.

Since corresponding sides of similar triangles are proportional,

`(UT)/(5)=(13.2+5)/(13)\\UT=(5)\left((13.2+5)/(13) \right)=\boxed{7}`