Question

If ΔABC ~ ΔPQR in which AB = 6 cm, BC = 4 cm, AC = 8 cm and PR = 6 cm, then find the length of (PQ + QR).

Answer 1

Since ΔABC ~ ΔPQR, their corresponding sides are proportional:

`(AB)/(PQ) = (BC)/(QR) = (AC)/(PR)`

`(AC)/(PR)= 8/6 = 4/3`

`(AB)/(PQ) = 4/3`

`PQ = 3/4 xx AB`

`PQ = 3/4 xx 6 = 4.5 cm`

`(BC)/(QR) = 4/3`

`QR = 3/4 xx BC`

`QR = 3/4 xx 4 = 3 cm`

PQ + QR

= 4.5 + 3 

= 7.5 cm