Question

triangle abc is an isosceles triangle right angled at B .equilateral triangle ACD and Abe are constructed on side AC and ab .prove that the ratio between the area of triangle ACD and triangle abe is 2:1

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.

∴ ar(ΔABE) : ar(ΔACD) = 1 : 2

Answer 2

Answer

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