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