Geometry-10 (CAT-2002)

In the following figure, the area of isosceles right triangle ABE is 7 sq.cm. If EC=3BE, then the area of
rectangle ABCD is (in sq.cm):

(1)64   (2)82   (3)26   (4)56

Solution follows here:

Solution:

Given that ABE is isosceles right triangle => AB = BE

∆ABE = ½ (base)(height) = ½ (BE)(AB) = 7

=> ½ (AB)² = 7 => AB = BE = √14

Given that EC=3BE => EC = 3√14

BC = BE+EC = √14+3√14 = 4√14

Area of rectangle = AB*BC = √14*4√14 = 4*14 = 56

Answer (4)