Question

Find the missing length. The triangles in each pair are similar.

Answer 1

UW = 117 , SR = 24

Explanation:

since the pairs of triangles are similar then the ratios of corresponding sides are in proportion.

(1)

Δ UML ≅ Δ UWV

`(UW)/(UM)` =
`(UV)/(UL)` ( substitute values )

`(UW)/(45)` =
`(104)/(40)` ( cross- multiply )

40 UW = 45 × 104 = 4680 ( divide both sides by 40 )

UW = 117

(2)

Δ SRT ≅ Δ KRJ

`(SR)/(KR)` =
`(ST)/(KJ)` ( substitute values )

`(SR)/(12)` =
`(16)/(8)` = 2 ( multiply both sides by 12 )

SR = 12 × 2 = 24