Question

Abc is an isosceles traingle right angled at B two equilateral traingles are constructed with sides BD and AC prove that areas of ∆BCD= 1/2 AR∆ACE

Answer 1

Given ΔABC is an isosceles triangle in which ∠B = 90° ⇒ AB = BC By Pythagoras theorem, we have AC2= AB2+ BC2 ⇒AC2= AB2+ AB2[Since AB = BC] ∴ AC2= 2AB2→ (1) It is also given that ΔABE ~ ΔACD Recall that ratio of areas of similar triangles is equal to ratio of squares of their corresponding sides.