The width of the rectangle is 20 cm and the length is 3 times the width.

| June 19, 2021 | education

The width of the rectangle is 20 cm and the length is 3 times the width. Find the area of a square whose perimeter is equal to the perimeter of this rectangle.

First, find the length of the rectangle if the length is 3 times the width and the width of the rectangle is 20 cm:

20 * 3 = 60 (cm).

Find the perimeter of a rectangle with sides of 20 cm and 60 cm, which is equal to the doubled sum of its two sides:

P = 2 (20 + 60) = 2 * 80 = 160 (cm).

By the condition of the problem, the perimeter of this rectangle is equal to the perimeter of the square, which means that the perimeter of the square is 160 cm.

Find the side length of a square by dividing its perimeter by the number of sides, that is, by 4:

160: 4 = 40 (cm).

Now we calculate the area of ​​a square with a side of 40 cm, having raised the length of its side to a square:

S = 40² = 1600 (cm²).

Answer: the area of ​​the square is 1600 cm².



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