Question

The length of a rectangle is 4 times than its width. the area of the rectangle is 1024cm2 find the length of the rectangle the perimeter of the rectangle 4 square has the same perimeter as that its rectangle. Find the area of the square.

Answer 1

1024cm^2=x×4x. 4x^2=1024cm^2. x^2=256. x=√256. x=16

Answer 2

The length of the rectangle is 64 cm.

The area of the square is 100 cm. sq.

Explanation:

Given : The length of a rectangle is 4 times than its width. The area of the rectangle is 1024 cm sq.

The perimeter of the rectangle 4 square has the same perimeter as that its rectangle.

To find : The length of the rectangle and Find the area of the square?

Solution :

Let l be the length of the rectangle.

Let w be the width of the rectangle.

The length of a rectangle is 4 times than its width i.e l=4w

The area of the rectangle is

`A=l* w`

`1024=4w* w`

`256=w^2`

`w=\pm 16`

Reject negative value.

The width of the rectangle is w=16 cm.

The length of the rectangle is

`l=4w\\l=4* 16\\l=64cm`

Therefore, The length of the rectangle is 64 cm.

Now, The perimeter of the rectangle 4 square has the same perimeter as that its rectangle.

Perimeter of the rectangle is
`P=2(l+b)`

`P=2(64+16)`

`P=2(80)`

`P=160`

Perimeter of rectangle divides into 4 squares.

i.e. Perimeter of one square is
`P=(160)/(4)=40`

Now, The side of the square is

`P=4s`

`40=4s`

`s=10`

The area of the square is
`A=s* s`

`A=10* 10`

`A=100cm^2`

Therefore, The area of the square is 100 cm. sq.