Let x = one of the legs.
Then, the other leg = x + 3.
Ed will use the Pythagorean Theorem to find the hypotenuse.
So, let a = x one leg. Let b= x + 3 the other leg. And, let c = 15 the hypotenuse.
The Pythagorean Theorem is:
c^2 = a^2 + b^2, where a and b are the legs and c is the hypotenuse.
We have:
15^2 = x^2 + (x + 3)^2
225 = x^2 + x^2 + 6x + 9
Rearranging:
2x^2 + 6x - 216 = 0
Divide by 2:
x^2 + 3x - 108 = 0
Solve by factoring:
(x - 9)(x + 12) = 0
So, x = 9 and x = -12. (x = -12 is not a valid answer.)
x = 9
x + 3 = 12
Conclusion: The legs of the right triangle are 9 inches and 12 inches.
Eddie-G…