The perimeters of the square and rectangle are equal. the area of the square is 81 cm2.

The perimeters of the square and rectangle are equal. the area of the square is 81 cm2. the length of the rectangle is 2 times its width. Find the area of the rectangle.

1) Find out the length of the side of the square if it is known that its area is 81 cm2.

√81 = 9 cm

or

81 = 9 * 9,

81: 9 = 9 cm.

2) Find out what the perimeter of the square is, if it is known that the length of its side is 9 cm.

(9 + 9) * 2 = 36 cm.

3) Let us denote the width of the rectangle by the letter X, then, according to the condition of the problem, where the length of the rectangle is 2 times the width, the length will be 2X. It is known that the perimeters of the square and the rectangle are equal, that is, 36 cm each. Let’s make an equation, solve it and find out what the width of the rectangle is.

(X + 2X) * 2 = 36,

3X * 2 = 36,

6X = 36, X = 36: 6,

X = 6.

4) Find out the length of the rectangle if it is known that it is 2 times the width.

6 * 2 = 12 cm.

5) We find out the area of ​​the rectangle if it is known that its length is 12 cm and its width is 6 cm.

12 * 6 = 72 cm2

Answer: the area of ​​the rectangle is 72 cm2.