The area of the rectangle is 56 cm². The distance from the point of intersection of the diagonals

The area of the rectangle is 56 cm². The distance from the point of intersection of the diagonals of the rectangle to one of its sides is 4 cm. Find the perimeter of the rectangle.

Since the diagonal of a rectangle divides it into two equal right-angled triangles, the distance from the point of intersection of the diagonals of the rectangle to one of its sides is equal to half the length of the other side. According to this, we can find one side of the rectangle:

4 * 2 = 8 cm – the length of one side of the rectangle.

Knowing the value of the area of the rectangle, we can find its second side:

56: 8 = 7 cm – the length of the second side of the rectangle.

We find the answer:

2 * (8 + 7) = 30 cm – the perimeter of the rectangle.

Answer: 30 cm.