The hypotenuse of a right triangle is 17cm, and the difference in length is 7cm. Find the length of each leg of this triangle.

We will write the initial data in the form a -?, B = a – 7 cm, c = 17 cm. For the solution, we will use the formula a² + b² = c² from the Pythagorean theorem. Substitute the values:

a² + (a – 7) ² – 17² = 0
a² + a² – 14 * a + 49 – 289 = 0
2 * a² – 14 * a – 240 = 0
a² – 7 * a – 120 = 0
D = 7² + 4 * 120 = 529
a = (7 + 23) / 2 = 15 cm; the root a2 = – 8 does not fit.
b = a – 7 = 15 – 7 = 8 cm

Answer: the legs are 15 and 8 cm.