Hi, there.
For this question, we can apply the Pythagorean theorem [tex]a^2 + b^2 = c^2[/tex].
I'm sure you've seen this equation before, and they kind of tried to trip you up with this problem. Trust me, it's easier than it looks. Let's break it down.
Lengths a and b both have the value of 48, which means that the value s in [tex]\sqrt{2s^2}[/tex] is 48, because the length of the hypotenuse is the same as the length and height squared multiplied by 2.
Plug in the value for c: [tex]a^2 + b^2 = (\sqrt{2s^2})^2[/tex]
Plug in the value for s:
[tex](\sqrt{2(48^2)})^2[/tex]
Do the innermost exponents first:
[tex](\sqrt{2(2304)})^2[/tex]
The square root symbol and the power of 2 cancel each other out, so we are left with:
s = [tex]2(2304)[/tex], so the hypotenuse is 4608 inches.
