The leg of a right-angled triangle is 3 cm, and the hypotenuse is 5 cm. Find the area of the triangle.

The solution of the problem:

1. Find the second leg of the triangle.

b ^ 2 = c ^ 2 – a ^ 2;

where c is the hypotenuse,

a and b – the legs of the triangle.

b ^ 2 = 5 ^ 2 – 3 ^ 2 = 25 – 9 = 16 cm;

b = √16 = 4.

2. Determine the area of the triangle.

S = 1/2 * a * b;

S = 1/2 * 3 * 4 = 12/2 = 6 cm2.

Answer: the area of the triangle is 6 cm2.