Hypatenuse AO of a right-angled triangle ABO is 13 cm and leg AB is 12 What is leg AB?

To solve the problem, it is necessary to use the Pythagorean theorem. In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the legs.

If in a right-angled triangle ABO, the BO leg is x, the AO hypotenuse is 13 cm, and the AB leg is 12 cm, then

AO ^ 2 = AB ^ 2 + BO ^ 2

or quadratic equation

13 ^ 2 = 12 ^ 2 + x ^ 2.

Whence, we express the square of the unknown quantity

x ^ 2 = 13 ^ 2 – 12 ^ 2;

x ^ 2 = 169 – 144;

x ^ 2 = 25.

Thus, the roots of the equation are

x (1) = -5 – does not make sense and

x (2) = 5 (cm).

Answer: leg VO = 5 cm.