ABCD is a square. F is the mid-point of AB. BE is one third of BC. If the area of ΔFBE = 108 cm 2 , find the length of AC.

Question

ABCD is a square. F is the mid-point of AB. BE is one third of BC. If the area of &Delta;FBE = 108 cm 2 , find the length of AC.

Philoid · Accepted Answer

According to the question, the figure is :

∵ ABCD is a square. Hence, AB = BC = CD = DA

∵ F is the midpoint of AB.

∴ Length of BF = AB/2 = BC/2 (∵ AB = BC)

Given that, BE = BC/3

In ΔFBE, ∠B = 90° and Area of ΔFBE = 108 cm²

⇒ BC² = 108 × 12

⇒ BC² = 36 × 36

⇒ BC = 36 cm²

AC is the diagonal of the ABCD.

⇒ AC = 36√2 = 50.904 cm