Answer:
x = 1/2
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^2 + (√2)^2 = (x + 1)^2
Then, we isolate x:
x^2 + 2 = (x + 1)(x + 1) = x^2 + 2x + 1
(Subtract x^2 from both sides)
2 = 2x + 1
(Subtract 1 from both sides, I also flipped the equation)
2x = 1
(Divide both sides by 2)
x = 1/2
To double-check, substitute x with 1/2:
(1/2)^2 + (√2)^2 = (1/2 + 1)^2
Simplify:
1/4 + 2 = 9/4
=> 1/4 + 8/4 = 9/4 (true)