Question

In two triangles ABC and DEF, ∠A = ∠D and the sum of the angles A and B is equal to the sum of the angles D and E. If BC = 6 cm and EF = 8 cm, then ar (ΔABC) : ar (ΔDEF) = ______.

Answer 1

In two triangles ABC and DEF, ∠A = ∠D and the sum of the angles A and B is equal to the sum of the angles D and E. If BC = 6 cm and EF = 8 cm, then ar (ΔABC) : ar (ΔDEF) = 9 : 16.

Explanation:

Since ∠A = ∠D and A + B = D + E, subtracting from 180° gives ∠C = ∠F; so two angles of ΔABC and ΔDEF are equal, hence the triangles are similar (AA).

Corresponding sides are proportional, so `(BC)/(EF) = 6/8 = 3/4`.

Areas scale as the square of the similarity ratio, so ar(ΔABC) : ar(ΔDEF) = `(3/4)^2` = 9 : 16.