Solve the equation using zero-product property

A) 2, -7

This is because you can view each (x-2) and (x+7) as a number. Thinking like this you have two numbers multiplied together to give you 0. The only way to multiply two numbers and get 0 is if either one or both of the numbers are 0. (As anything times 0 is 0.) So:

(x - 2) could be 0   or   (x + 7) could be 0

Mathematically:

x - 2 = 0           and            x+ 7 =0
   +2    +2                               -7   -7
x = 2                                  x = -7

The third side is approximately 31.6 inches long.

Step-by-step explanation:

When given the lengths of two sides of a right triangle, you can easily use Pythagorean Theorem (a2+b2=c2; a or b being the legs, c being the hypotenuse) to find the length of the third side. Since the legs (10 in. and 30 in.) are already given to us, we can simply insert the numbers into Pythagorean Theorem and solve for the third side! It should look a little something like this: 102+302=c2, then solve for the squares to get 100+900=c2, then add the two side lengths to get to 1,000=c2, then find the square root of both sides (now, since the c is already being squared, they will cancel out to just c, but you will get the actual square root of 1,000). Should all go well, you should get an answer of 31.6227766017, which just so happens to round out to 31.6. And with that, we have our final no-longer-missing side length of 31.6 inches.

Hope this helped!