Question

a rectangle with diagonal of length 20cm has sides in the ratio of 2:1 .find the area of the rectangle

Answer 1

Let the length =2x
and breath = 1x
diagonal = 20cm

20² = (2x)² + (1x)²     [ by Pythagoras thm ]
400 = 4x² + 1x²
400 = 5x²
x² = 400/5
x² = 80
x =√80
x = √2×2×2×2×5
x = 4√5
∴length =2x = 2×4√5 = 8√5
   breath = 1x= 4√5

∴ area of a rectangle = l×b
                                  = 8√5 × 4√5
                                     =32 ×5
                                     = 160

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Answer 2

let the length be 2x
and the breadth be x
diagonal=20cm (given)
diagonal of rectangle=√l^2+b^2
20cm=√2x^2+x^2
400cm=4x+x
400cm=5x
x=80cm
length=2x=2×80=160cm
breadth=x=80cm
Area of rectangle=l×b
= 160cm×80cm
= 12800cm^2