Find the perimeter of a right-angled triangle if its hypotenuse is 17 and the difference between the legs is 7.

Let x be the length of the smaller leg, then the second leg will have a length (x + 7). By the condition of the problem, the triangle is right-angled; therefore, the Pythagorean theorem is applicable.
x ^ 2 + (x + 7) ^ 2 = 17 ^ 2
2x ^ 2 + 14x – 240 = 0
x ^ 2 + 7x – 120 = 0
D = b2 – 4ac
D = 49 + 480 = 529.
x = (-b ± √D) / 2a
x = (-7 ± 23) / (2 * 1)
x1 = 8, x2 = -15.
The length of the leg cannot take a negative value, x2 = -15 is not a solution to the problem.
8 + 7 = 15 – second leg.
Find the perimeter: 8 + 15 + 17 = 40.
Answer: The perimeter of the triangle is 40.