Question

If ΔАВС ~ ΔEDF and given that AB = 5 cm, BC = 6.25 cm, DF = 15 cm, and EF = 16.8 cm, find AC and DE.

Answer 1

Given:

△ABC ∼ △EDF

So, the corresponding sides are:

AB ↔ ED, BC ↔ DF, AC ↔ EF

Thus,

`(AB)/(ED) = (BC)/(DF) = (AC)/(EF)`

Here the ratio is:

`(BC)/(DF) = 6.25/15 = 5/12`

⇒ Let’s find AC:

`(AC)/(EF) = 5/12`

`AC = 5/12 xx 16.8`

∴ AC = 7 cm

⇒ Let’s find DE:

`(AB)/(ED) = 5/12`

`ED = 12/5 xx 5`

∴ ED = 12 cm

Hence, AC = 7 cm and DE = 12 cm.