In order to find the answer to this one, we're going to need to do a lot of algebra. First of all, remember that a rectangle has two sets of congruent sides, which make the perimeter when put together. I'll define the two different measurements (one for one set, one for the other set) as l and w. Therefore, 2l + 2w = P, or the two sets of congruent sides equal the perimeter.
In this problem, l = x + 12 and w = 2x + 8. The perimeter is 18x - 20. Let's plug these values into our earlier equation.
2(x + 12) + 2(2x + 8) = 18x - 20 Substitution 2x + 24 + 4x + 16 = 18x - 20 Distribute 6x + 40 = 18x - 20 Combine like terms 6x = 18x - 60 Subtract 40 from both sides -12x = -60 Subtract 18x from both sides x = 5 Divide both sides by -12
Therefore, x = 5. Let's plug that in to l (x + 12) and w (2x + 8) to find the side lengths.