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

Answer:

Area of the square is 2916 $m^{2}$.

Step-by-step 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 = $\sqrt{324}$

   = 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 = $\frac{216}{4}$

 = 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 $m^{2}$.