Question

In the adjacent figure, ∆ACB ~ ∆APQ. If BC = 8 cm, PQ = 4 cm, BA = 6.5 cm and AP = 2.8 cm, find CA and AQ

Answer 1

Given ∆ACB ~ ∆APQ

`"AC"/"AP" = "BC"/"PQ" = "AB"/"AQ"`

`"AC"/2.8 = 8/4 = 6.5/"AQ"`

Consider `"AC"/2.8 = 8/4`

4AC = 8 × 2.8

AC = `(8 xx 2.8)/4` = 5.6 cm

Consider `8/4 = 6.5/"AQ"`

8AQ = 4 × 6.5

AQ = `(4 xx 6.5)/8` = 3.25 cm

Length of AC = 5.6 cm, Length of AQ = 3.25 cm