Answer:
x = 225
Explanation:
Pythagorean Theorem: a^2 + b^2 = c^2, where a and b are the side lengths and c is the hypotenuse.
Substituting in the values:
(x - 3)^2 + 9^2 = x^2
Then, we isolate x:
(x - 3)^2 + 81 = (x - 3)(x - 3) + 81 = x^2 - 6x + 9 + 81 = x^2 - 6x + 90 = x^2
(Subtract x^2 from both sides)
- 6x + 90 = 0
(Add 6x to both sides, I also flipped the equation to put x on the left side)
6x = 90
(Divide both sides by 6)
x = 15
To double-check, substitute x with 15:
(15 - 3)^2 + 9^2 = 15^2
Simplify:
144 + 81 = 225 (true)