Answer:
Area of the square is 2916 [tex]m^{2}[/tex].
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[tex]w^{2}[/tex]
divide through by 5 to have,
[tex]w^{2}[/tex] = 324
w = [tex]\sqrt{324}[/tex]
= 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 = [tex]\frac{216}{4}[/tex]
= 54
length of the side of square is 54 m.
Therefore,
Area of square = [tex]l^{2}[/tex]
= [tex]54^{2}[/tex]
= 2916
Area of the square whose perimeter is equal to that of the rectangle is 2916 [tex]m^{2}[/tex].
