Find the area and perimeter of a rectangle with a diagonal of 17 cm and a side of 15 cm.

In order to calculate the area and perimeter, you need to know both the length and the width of the rectangle. We know that the diagonal = 17, and the length = 15, we find the width from a right-angled triangle with hypotenuse 17 and leg 15:

15 ^ 2 + x ^ 2 = 17 ^ 2

x ^ 2 = 17 ^ 2-15 ^ 2

x ^ 2 = 289-225 = 64

x = 8

Now, knowing both the length and the width of the rectangle, we find the perimeter P and the area S:

P = 15 + 15 + 8 + 8 = 46cm

S = 15 * 8 = 90 cm ^ 2