In a rectangle, one side is 3 times smaller than the other and the area is 48 cm.

In a rectangle, one side is 3 times smaller than the other and the area is 48 cm. Find the area of the square built on the larger side of the rectangle.

1) Find the sides of the rectangle.

Let one side of the rectangle be x cm, then the second side of the rectangle is 3x cm. The area of ​​the rectangle is equal to the product of its sides, i.e. x * 3x cm ^ 2 or 48 cm ^ 2. Let’s make an equation and solve it.

x * 3x = 48;

3x ^ 2 = 48;

x ^ 2 = 48: 3;

x ^ 2 = 16;

x1 = 4; x2 = – 4 – the side of the rectangle cannot be negative, so one side is 4 cm.

3x = 3 * 4 = 12 (cm) – the length of the second side.

2) Find the area of ​​the square built on the larger side of the rectangle.

If the square is built on the larger side of the rectangle, and the larger side is 12 cm, then this means that the side of this square is also 12 cm.

The area of ​​a square is equal to the square of its side S = a ^ 2 = a * a.

12 ^ 2 = 144 (cm ^ 2)

Answer. 144 cm ^ 2.