Answer:
Explanation:
Let x be the length of the shorter leg of the triangle.
Then, the longer leg is 7 inches longer, which means its length is x + 7.
Using the Pythagorean theorem, we can write:
x^2 + (x + 7)^2 = 35^2 => x^2 + x^2 + 14x + 49 = 1225
Expanding the squares and simplifying, we get:
2x^2 + 14x - 576 = 0
We can solve for x by using the quadratic formula:
x = (-14 ± √(14^2 - 4(2)(-576))) / (2(2))
x = (-14 ± √(3968)) / 4
x ≈ 12.8 or x ≈ -17.8
Since x represents the length of a side of a triangle, it must be positive. Therefore, we take x ≈ 12.8 as the solution.
The lengths of the legs of the triangle are x ≈ 12.8 inches and x + 7 ≈ 19.8 inches.
So, the lengths of the legs of the triangle are approximately 12.8 inches and 19.8 inches.