Answer:
x=4
Explanation:
We can use the Pythagorean theorem to find x
a^2 +b^2 =c^2
where a and b are the legs and c is the hypotenuse.
x^2 +x^2 = (4sqrt(2))^2
Combine like terms
2x^2 = (4sqrt(2))^2
We know (ab)^2 = a^2 * b^2
2x^2 = (4)^2 *(sqrt(2))^2
2x^2 = 16 *2
Divide by 2
2x^2/2 = 16*2/2
x^2 =16
Take the square root of each side
sqrt(x^2) = sqrt(16)
x = ±4
x=4
We only take the positive square root since lengths cannot be negative