Question

ΔАВС ~ ΔРQR, ar(ΔABC) = 16 cm², ar(ΔPQR) = 144 cm² and PQ = 6 cm, then the length of BA is ______.

Options

• 1 cm

• 2 cm

• 3 cm

• 4 cm

Answer 1

ΔАВС ~ ΔРQR, ar(ΔABC) = 16 cm², ar(ΔPQR) = 144 cm² and PQ = 6 cm, then the length of BA is 2 cm.

Explanation:

Since △ABC ∼ △PQR, the ratio of their areas is equal to the square of the ratio of corresponding sides:

`"ar(ΔABC)"/"ar(ΔPQR)" = ((AB)/(PQ))^2`

Given,

`16/144 = ((AB)/6)^2`

`1/9 = ((AB)/6)^2`

`(AB)/6 = sqrt(1/9)`

`(AB)/6 = 1/3`

`AB = 6/2`

∴ AB = 2 cm