Question

In the diagram below, RA is parallel to ET, and RT is 21 units long. Find the length of ST.

Answer 1

ST = 12 units

Explanation:

Δ STE and Δ SRA are similar ( AA postulate ) , then the ratios of corresponding sides are in proportion, that is

`(ST)/(SR)` =
`(TE)/(RA)` ( substitute values )

`(ST)/(21-ST)` =
`(8)/(6)` ( cross- multiply )

6 ST = 8(21 - ST)

6 ST = 168 - 8 ST ( add 8 ST to both sides )

14 ST = 168 ( divide both sides by 14 )

ST = 12 units