Calculate the area of a rectangle whose diagonal is 10 cm long and one side is 8 cm long

1) Find the second side of the rectangle.

The sides of a rectangle and its diagonal form a right-angled triangle. The diagonal will be the hypotenuse of this triangle, and the sides will be the legs. We apply the Pythagorean theorem to this triangle: In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the legs. The unknown leg is denoted by x.

x ^ 2 + 8 ^ 2 = 10 ^ 2;

x ^ 2 + 64 = 100;

x ^ 2 = 100 – 64;

x ^ 2 = 36;

x = 6 (cm).

2) Find the area of the rectangle.

The area of a rectangle is equal to the product of its sides. S = ab.

S = 6 * 8 = 48 (cm ^ 2)

Answer. 48 cm ^ 2.