Question

the length of a rectangle is 5 times as long as its breadth and its area is 1620 m² find area of square whose perimeter is equal to that of a rectangle​

Answer 1

Area of the square is 2916
`m^(2)`.

Explanation:

Let the breadth of the rectangle be represented by w. So that;

length of rectangle = 5w

Area of rectangle = length x breadth

= 5w x w

1620 = 5
`w^(2)`

divide through by 5 to have,

`w^(2)` = 324

w =
`√(324)`

= 18

Thus, the breadth of the rectangle is 18 m.

length = 5 w = 5 x 18

= 90 m

The length of the rectangle is 90 m.

Perimeter of the rectangle = 2(l + w)

= 2( 90 + 18)

= 216 m

Perimeter of a square = 4l

where l is the length of its side.

Given that the perimeters of the rectangle and square are equal, then;

4l = 216

l =
`(216)/(4)`

= 54

length of the side of square is 54 m.

Therefore,

Area of square =
`l^(2)`

=
`54^(2)`

= 2916

Area of the square whose perimeter is equal to that of the rectangle is 2916
`m^(2)`.