Answer:
So the lengths of the legs are approximately 8.6 cm and 15.6 cm.
Explanation:
Let's call the smaller leg "x" and the larger leg "x + 7". According to the Pythagorean theorem, we know that:
x^2 + (x + 7)^2 = 17^2
Expanding the square on the left side and simplifying, we get:
2x^2 + 14x - 210 = 0
Dividing both sides by 2, we get:
x^2 + 7x - 105 = 0
Now we can solve for x using the quadratic formula:
x = (-7 ± sqrt(7^2 - 4(1)(-105))) / 2(1)
x = (-7 ± sqrt(649)) / 2
x ≈ -15.6 or x ≈ 8.6
Since we're dealing with lengths of sides in a triangle, we can't have a negative value for x. So we discard the negative solution and conclude that the smaller leg is approximately 8.6 cm.
To find the larger leg, we add 7 to x:
x + 7 ≈ 15.6 cm