One of the legs of a right-angled triangle is 2 cm larger than the other, and the hypotenuse is 10 cm

One of the legs of a right-angled triangle is 2 cm larger than the other, and the hypotenuse is 10 cm. Find the area of the triangle.

A variable is required to accomplish this task.
1. Let x cm – the length of the first leg;
2. Then (x + 2) cm is the length of the second leg.
3. We express x through the Pythagorean theorem:
x ^ 2 + (x + 2) ^ 2 = 102;
x ^ 2 + x ^ 2 + 4 + 4x = 100;
2x ^ 2 + 4x – 96 = 0;
x ^ 2 + 2x – 48 = 0;
Let’s solve the quadratic equation through the discriminant:
D = b ^ 2 – 4 * a * c = 4 + 192 = 196 = 14 ^ 2;
x1 = (-2 + 14) / 2 = 6;
x2 = (-2 – 14) / 2 = -8 – is not a solution;
the first leg = 6 cm, the second – 8 cm.
4. Find the area:
6 * 8/2 = 24 (cm2);
Answer: 24 cm2