In a rectangle, one side is 3 times smaller than the other, and the area is 48 cm².

In a rectangle, one side is 3 times smaller than the other, and the area is 48 cm². Find the area of the square built on the larger side of the rectangle.

1) Knowing that one side is 3 times smaller than the other, and the area is 48 cm², we will compose a system of equations for finding the sides.

x = 3y;

x * y = 48;

Then:

3y * y = 48;

Therefore 3y² = 48.

16 = y²;

y = 4 cm.

Then x:

x = 3y;

x = 3 * 4;

x = 12 cm.

2) Find the area of the square of the larger side.

12 * 12 = 144 cm².

Answer: The area of the square located on the larger side of the rectangle is 144 centimeters.