Question

The perimeter of a rectangle is 62m. find the length of its sides if it is known that the area of the rectangle is 1980000 cm².

Answer 1

The perimeter of a rectangle is 62m. find the length of its sides if it is known that the area of the rectangle is 1980000 cm².

Answer 2

L=22 m or L=9 m

Explanation:

We are given that

Perimeter of rectangle=62 m

Area of rectangle =
`1980000cm^2=198m` (1m=100 cm)

We have to find the lengths of its sides.

Let Length of rectangle =x

Breadth of rectangle=y

Perimeter of rectangle=2(x+y)

Area of rectangle =xy

According to question

`2(x+y)=62`

`x+y=(62)/(2)=31`

`xy=198`

`y=(198)/(x)`

Substitute the value of y

`x+(198)/(x)=31`

`(x^2+198)/(x)=31`

`x^2+198=31x`

`x^2-31x+198=0`

`x^2-22x-9x+198=0`

`x(x-22)-9(x-22)=0`

`(x-22)(x-9)=0`

`x-22=0\implies x=22`

`x-9\implies x=9`

Substitute the value x=22

`y=(198)/(22)=9`

Substitute the value of x=9

`y=(198)/(9)=22`

Hence, the length of sides of rectangle are

x=22 m and x=9 m