Answer:
Using the Pythagorean Theorem - (leg #1)² + (leg #2)² = hypotenuse² - you can find that [tex]x=17[/tex].
Step-by-step explanation:
The Pythagorean Theorem states that, for every right triangle with legs a and b and hypotenuse c, these sides are related by the equation [tex]a^2+b^2=c^2[/tex]. Using [tex]x-2[/tex] and 8 as our legs and [tex]x[/tex] as our hypotenuse, we can substitute to obtain the equation
[tex](x-2)^2+8^2=x^2[/tex]
From here, we can expand [tex](x-2)^2[/tex] into the expression [tex]x^2-4x+4[/tex] and simplify 8² to 64, giving us
[tex]x^2-4x+4+64=x^2[/tex]
Combining like terms:
[tex]x^2-4x+68=x^2[/tex]
Since we have an [tex]x^2[/tex] on both sides, we can subtract it away to eliminate it:
[tex]-4x+68=0[/tex]
Adding 4x to both sides:
[tex]68=4x[/tex]
And finally dividing both sides by 4:
[tex]17=x\\x=17[/tex]
