Question

ABC is right angled triangle at A. AGFB is a square on the side AB and BCDE is a square on the hypotenuse BC. If AN is perpendicular to ED. Prove that area of square AGFB is equal to the area of the rectangle BENM

Answer 1

Area of rectangle BENM = Area of Square  AGBF

Step-by-step explanation:

Area of Square  AGBF

= BA * BA

= BA²

Area of rectangle BENM

= BE * BM

BE = BC  as BCDE is a sqaure

= BC * BM

AM ⊥ BC

ΔBMA & ΔBAC

∠B = ∠B  ( common angle)

∠BMA = ∠BAC = 90°

=> ΔBMA ≈ ΔBAC

=>  BM/BA  = MA/AC  = BA/BC

BM/BA  = BA/BC

=> BM * BC = BA²

Area of rectangle BENM =  BA²

Area of Square  AGBF = BA²

=> Area of rectangle BENM = Area of Square  AGBF

QED

Proved

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