length =24, width =15
1) The best way to tackle this question is by sketching this out:
2) We can think of it as a rectangle whose area is 360yd². Since the farmer has 54 yds we can write out this:
We can set two equations: one evolving the sum of three sides and the other one the area:
[tex]\begin{gathered} 2b+h=54 \\ bh=360 \\ ----- \\ 2b=54-h\Rightarrow b=27-\frac{h}{2} \\ bh=360 \\ (27-\frac{h}{2})h=360 \\ \\ 27h-\frac{h^2}{2}=360 \\ -\frac{h^2}{2}+27h-360=0 \\ \frac{h^2}{2}-27h+360=0 \\ h=\frac{27\pm\sqrt[]{(27)^2-4(\frac{1}{2})(360)}}{2(\frac{1}{2})} \\ h=24 \\ --- \\ 2b+24=54 \\ 2b=54-24 \\ 2b=30 \\ b=15 \end{gathered}[/tex]
