Question

The area of a rectangle is 504 square meters. If the perimeter is 90 meters, find the length and width of the rectangle.

Answer 1

Length =24m and width = 21m

Explanation:

Given,

Area of rectangle, A = 504 m^2

Perimeter of rectangle, P = 90 m

Since we know, A = Length * width and P = 2(Length + width)

So, A = L * w

=> 504 = L*w ------------------(1)

And P = 2(L + w)

=> 90 =2( L + w) ----------------(2)

Plug L =504/w in equation 2

i.e. 90 = 2( 504/w + w)

or 45 = 504/w + w

or 45 = (504 + w^2 ) / w

or 45w = 504 + w^2

or w^2 - 45w + 504 = 0

On solving above quadratic equation we get:

w = 21 or 24

So we take width , w= 21 meter

Then length will be, L =504/21 =24 meter

Hence length and width of rectangle are 24m and 21m respectively.