Question

What is the value of x?​

Answer 1

`\large\boxed{x=8\sqrt2}`

Explanation:

`\bold{METHOD\ 1}\\\\\text{Use the Pythagorean theorem:}\\\\leg^2+leg^2=hypotenuse^2\\\\\text{We have}\ leg=8,\ leg=8,\ hypotenuse=x.\\\text{Substitute:}\\\\x^2=8^2+8^2\\\\x^2=2(8^2)\to x=√(2(8^2))\qquad\text{use}\ √(ab)=√(a)\cdot√(b)\\\\x=\sqrt2\cdot√(8^2)\qquad\text{use}\ √(a^2)=a\\\\x=8\sqrt2`

`\bold{METHOD\ 2}\\(look\ at\ the\ picture)\\\\\text{We have}\ a=8.\ \text{Therefore}\ a\sqrt2=8\sqrt2`