You can write the dimensions of the rectangle as (x + 2) and (x - 5), and because the area is base × height, you can multiply the brackets together and make it equal to 56:
(x + 2)(2x - 5) = 56
2x² + 4x - 5x - 10 = 56
x² - x - 10 = 56
Now because you have an x², you need to make the equation equal to 0 so you can factorise, so:
2x² - x - 10 = 56
- 56
2x² - x - 66 = 0
(x - 6)(2x + 11)
So x is 6, because the other option is -5.5 and you cannot have a negative length.
I hope this helps!
keeping in mind that standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
![\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{\cfrac{6}{7}}[x-\stackrel{x_1}{(-3)}]\implies y+1=\cfrac{6}{7}(x+3) \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{7}}{7(y+1)=7\left( \cfrac{6}{7}(x+3) \right)}\implies 7y+7=6(x+3)\implies 7y+7=6x+18 \\\\\\ 7y=6x+11\implies -6x+7y=11\implies 6x-7y=-11](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Barray%7D%7B%7Cc%7Cll%7D%20%5Ccline%7B1-1%7D%20%5Ctextit%7Bpoint-slope%20form%7D%5C%5C%20%5Ccline%7B1-1%7D%20%5C%5C%20y-y_1%3Dm%28x-x_1%29%20%5C%5C%5C%5C%20%5Ccline%7B1-1%7D%20%5Cend%7Barray%7D%5Cimplies%20y-%5Cstackrel%7By_1%7D%7B%28-1%29%7D%3D%5Cstackrel%7Bm%7D%7B%5Ccfrac%7B6%7D%7B7%7D%7D%5Bx-%5Cstackrel%7Bx_1%7D%7B%28-3%29%7D%5D%5Cimplies%20y%2B1%3D%5Ccfrac%7B6%7D%7B7%7D%28x%2B3%29%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bmultiplying%20both%20sides%20by%20%7D%5Cstackrel%7BLCD%7D%7B7%7D%7D%7B7%28y%2B1%29%3D7%5Cleft%28%20%5Ccfrac%7B6%7D%7B7%7D%28x%2B3%29%20%5Cright%29%7D%5Cimplies%207y%2B7%3D6%28x%2B3%29%5Cimplies%207y%2B7%3D6x%2B18%20%5C%5C%5C%5C%5C%5C%207y%3D6x%2B11%5Cimplies%20-6x%2B7y%3D11%5Cimplies%206x-7y%3D-11)
The answer is A) x(2x+12)
I'm just gonna say 37 feet each due to it being 74ft to begin with.
Simple math xd
