Question

In the following figure, DE || BC, AD = 4 cm, AB = 10 cm, BC = 12 cm, and AE = 6 cm, find AC and DE.

Answer 1

Since DE || BC, triangles △ADE and △ABC are similar.

So, `(AD)/(AB) = (AE)/(AC) = (DE)/(BC)`

Given: AD = 4, AB = 10, AE = 6, BC = 12

Thus, `(AD)/(AB) = 4/10 = 2/5`

⇒ Let’s find AC:

`(AE)/(AC) = 2/5`

`6/(AC) = 2/5`

`AC = (6 xx 5)/2`

∴ AC = 15 cm

⇒ Let’s find DE:

`(DE)/(BC) = 2/5`

`(DE)/12 = 2/5`

`DE = (12 xx 2)/5`

`DE = 24/5`

∴ DE = 4.8 cm

Hence, AC = 15 cm and DE = 4.8 cm.