Question

For Exercises 5 and 6, use the triangles shown.
5. What is FE?
6. What is DE?

Answer 1

FE = 43.2 , DE = 48

Explanation:

Δ RQP and Δ EFD are similar , by the AA postulate , then the ratios of corresponding sides are in proportion , that is

(5)

`(FE)/(QR)` =
`(DF)/(PQ)` ( substitute values )

`(FE)/(36)` =
`(24)/(20)` ( cross- multiply )

20FE = 36 × 24 = 864 ( divide both sides by 20 )

FE = 43.2

Similarly

(6)

`(DE)/(PR)` =
`(DF)/(PQ)` ( substitute values )

`(DE)/(40)` =
`(24)/(20)` ( cross- multiply )

20DE = 40 × 24 = 960 ( divide both sides by 20 )

DE = 48