Question

If ΔABC ~ ΔPQR, AB : PQ = 4 : 5 and A(ΔPQR) = 125 cm², then find A(ΔABC).

Answer 1

Given: ΔABC ~ ΔPQR

We know that,

`("A"(Δ"ABC"))/("A"(Δ"PQR")) =  ("AB")^2/("PQ")^2`  ...[Theorem of area of similar triangles]

∴ `("A"(Δ"ABC"))/125 = (4)^2/(5)^2`

∴ `("A"(Δ"ABC"))/125 = 16/25`

∴ A(ΔABC) = `16/25 xx 125`

∴ A(ΔABC) =  80 cm²