The side lengths of a right-angled triangle are consecutive even numbers. Find the area of the triangle.

Let’s designate the smaller leg of the triangle a. Then the second leg
(a + 2), hypotenuse (a + 4). By the Pythagorean theorem:

a ^ 2 + (a + 2) ^ 2 = (a + 4) ^ 2;

a ^ 2 + a ^ 2 + 4a + 4 = a ^ 2 + 8a + 16;

a ^ 2 – 4a – 12 = 0;

D = (- 4) ^ 2 – 4 * 1 * (- 12) = 16 + 48 = 64.

a1 = (4 + 8) / 2 = 6;

a2 = (4 – 8) / 2 = -2 – we are not interested in the negative root.

Let’s calculate the area of the triangle:

S = 6 * (6 + 2) / 2 = 24.