One leg of the Pythagorean triangle is 15 dm, and about the second it is known that it is 3 dm

One leg of the Pythagorean triangle is 15 dm, and about the second it is known that it is 3 dm less than the hypotenuse, find the unknown sides of the triangle.

1. A, B, C – the vertices of the triangle. Angle A = 90 degrees. AB = 15 decimeters.

2. By the condition of the problem, the AC is less than the BC by 3 decimeters. BC = AC + 3 decimetres.

3. AC² + AB² = BC² (by the Pythagorean theorem).

4. Substitute in this expression (AC + 3) instead of BC:

AC² + 15² = (AC + 3) ².

AC² + 225 = AC² + 6AC + 9.

6AC = 216.

AC = 36 decimeters.

BC = 36 + 3 = 39 decimeters.

Answer: AC leg = 36 decimetres, BC hypotenuse = 39 decimetres.