The area of a right-angled triangle is 24. One of its legs is 2 larger than the other. Find the smaller leg.

1. Vertices of the triangle – А, В, С. АС is more than AB by 2 units. ∠А = 90 °.

S – area.

2. We take the length of the leg AB as x, the length of the other leg AC – x + 2.

3. Using the formula for calculating the area, we compose the equation:

x (x + 2) = 24;

x² + 2x – 24 = 0;

The first value of x = (- 2 + √4 + 96) / 2 = (-2 + 10) / 2 = 4.

The second value is x = (- 2 – 8) / 2 = – 5. Does not satisfy the condition of the problem.

AB = 4 units.

AC = 4 + 2 = 6 units.

Answer: AB = 4 units of measure – smaller leg.