Question

A farmer has 810 yd of fencing to enclose a rectangular pasture for her goats. Since one side of the pasture borders a river, thatside does not need to be fenced. Side b must be four times as long as side a. Find the dimensions of the rectangular pasture.

Answer 1

$a=135ft\:b=540ft$

1) We can tackle this question by writing out the following equation for the Perimeter of that fence:

$\begin{gathered} 2a+b=810 \\ b=4a \end{gathered}$

2) So now, let's plug into the 1st equation the second one, solving that system by the Substitution Method:

$\begin{gathered} 2a+4a=810 \\ 6a=810 \\ \frac{6a}{6}=\frac{810}{6} \\ a=135 \end{gathered}$

And finally, we can plug the quantity of "a" into the 2nd equation and solve it for b:

$\begin{gathered} b=4(135) \\ b=540 \end{gathered}$

3) Thus the answer is:

$\begin{gathered} a=135ft \\ b=540\:ft \end{gathered}$