Question

What is the value of x if this is a right triangle?

Answer 1

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