Find the area of a right-angled triangle if one of its legs is 12 and the hypotenuse is 13.

From the condition it is known that the hypotenuse is 13, and one of the legs is 12. In order to find the area of a right-angled triangle, we will use the following formula:

S = 1/2 * a * b, where a and b are the legs of a right-angled triangle.

Let’s use the Pythagorean theorem to find the length of the second leg.

The square of the hypotenuse is equal to the sum of the squares of the legs.

a ^ 2 + b ^ 2 = c ^ 2;

12 ^ 2 + x ^ 2 = 13 ^ 2;

144 + x ^ 2 = 169;

x ^ 2 = 169 – 144;

x ^ 2 = 25;

x = 5.

We are looking for the area of a right triangle:

S = 1/2 * 12 * 5 = 30 sq. units.

Answer: 30 sq. units.