Question

One of the diagonals of a rectangle a 20 cm long. The difference between its length and its width is 4 cm. Find the area of the rectangle?

Answer 1

A = 192 cm²

Explanation:

Given that,

The length of the diagonal of a rectangle is 20 cm.

The difference between its length and its width is 4 cm.

Let the length is l and width is b.

ATQ,

l-b = 4 ...(1)

Let x is the diagonal of the rectangle such that,

`x^2=l^2+b^2`

or

`20^2=l^2+b^2\\\\l^2+b^2=400` ....(2)

Now we need to solve equation (1) and (2).

Squaring equation (1) :
`l^2+b^2-2lb=16`

Put equation (2) in above equation.

`400-2lb=16\\\\400-16=2lb\\\\2lb=384\\\\lb=192`

Since, the area of the rectangle, A = lb

A = 192 cm²