In a right-angled triangle, one leg is 8 cm smaller than the other. Find the larger leg if the hypotenuse is 40 cm.

1. A, B, C – the vertices of the triangle. ∠А = 90 °. BC = 40 cm.

2. AB is less than AC by 8 cm. AC = AB + 8 cm.

3. Take the length of the leg AB as x. AC leg = x + 8.

4. Let’s make the equation:

x² + (x + 8) ² = 40² (by the Pythagorean theorem).

x² + x² + 16x + 64 = 1600;

2x² + 16x – 1536 = 0;

x² + 8x – 768 = 0;

The first value x = (- 8 + √64 + 4 x 768) / 2 = (- 8 + √3136) / 2 = (- 8 + 56) / 2 = 24 cm.

The second value is x = (- 8 – 56) / 2 = – 32 cm. Not accepted.

AB = 24 cm.

AC = 24 + 8 = 32 cm.

Answer: AC = 32 cm – larger leg.