Question

Triangles ABC and DEF are similar. If the length of the perpendicular AP from A on the opposite side BC is 2 cm and the length of the perpendicular DQ from D on the opposite side EF is 1 cm, then what is the area of △ABC?

(a) One and half times the area of the triangle DEF.

(b) Four times the area of triangle DEF.

(c) Twice the area of the triangle DEF.

(d) Three times the area of triangle DEF.

Answer 1

Correct option is (b) Four times the area of triangle DEF.

Areas of similar triangles are in the ratio of square of altitues.

\(\frac{Ar(\triangle ABC)}{Ar(\triangle DEF)} = \frac{AP^2}{DQ^2}\)

⇒ Ar(△ABC) = 4Ar(△DEF)