Question

The perimeter of rectangle is 56cm and length of diagonal is 20cm .Find length and breadth of rectangle.

Answer 1

1

What are the sides of a rectangle if we know that the perimeter is 56cm and the diagonal is 20cm?

Hungenahalli Sitaramarao Badarinath

Answered December 10, 2017

Let the sides of the rectangle be l and w.

Now 2(l+w) = 56, or l+w = 28 …(1)

The diagonal = [l^2 + w^2]^0.5 = 20, or

l^2 + w^2 = 20^2 = 400 …(2)

Square (1) to get (l+w)^2 = 28^2, or

l^2 + 2lw + w^2 = 784, but l^2 + w^2 = 400, hence

2lw = 784–400 = 384, or

lw = 384/2 = 192

One pair of l and w that give us a product of lw = 192 are

16 and 12.

So l = 16 and w = 12, the perimeter of the rectangle is 28 and the diagonal = [16^2+12^2]^0.5 = [256+144)^0.5 = 400^0.5 = 20.

The sides of the rectangle are 16 cm and 12 cm.