Find the area and perimeter of a rectangle if the diagonal is 13 cm and the bottom base is 12 cm.

We are given a rectangle. It is known that its diagonal is 13 cm, and it is also known that the lower base is 12 cm. And we need to find the perimeter and area of the rectangle.

To do this, we will apply the formulas:

S = a * b;

P = 2 (a + b).

The length of the rectangle is b = 12 cm, it remains to find the width. To calculate the width of a rectangle, consider a right-angled triangle formed by the sides of the rectangle and the diagonal.

a = √ (13 ^ 2 – 12 ^ 2) = √ (169 – 144) = √25 = 5 cm.

S = 5 * 12 = 60 cm ^ 2;

P = 2 (5 + 12) = 2 * 17 = 34 cm.