Question

Find the length of ST

Answer 1

ST = 10

Explanation:

Δ RSQ and Δ RTP are similar by the AA postulate , then

the ratios of corresponding sides are in proportion , that is

`(RS)/(RT)` =
`(RQ)/(RP)` ( substitute values )

`(5)/(RT)` =
`(9)/(9+18)` =
`(9)/(27)` =
`(1)/(3)` ( multiply both sides by 3 to clear the fraction )

RT = 3 × 5 = 15

Then

ST = RT - RS = 15 - 5 = 10