The length of the rectangle is 16 cm and the width is 4 times less, find the area of the square

| June 14, 2021 | education

The length of the rectangle is 16 cm and the width is 4 times less, find the area of the square in which the perimeter is equal to the perimeter of the rectangle.

The perimeter of a rectangle is the sum of all its sides, since the opposite dimensions of such a figure are equal, it corresponds to the formula:

P = 2a + 2b.

Let’s find this value, provided that the length = 16 cm, and the width is 4 times shorter (16: 4 = 4 cm):

P = 2 * 16 + 2 * 4 = 32 + 8 = 40 cm.

A square has all sides equal and its perimeter is calculated by the formula:

P = 4a.

If this value is also 40 cm, you can express “a” – the second factor, to find it, we divide the product by the first:

a = 40: 4 = 10 cm – side of the square.

Let’s calculate its area:

S = a² = 10 * 10 = 100 cm².



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