A farmer builds a fence to enclose a rectangular pasture.He uses 155 feet of fence. Find the total area of the pasture if it is 45.5 feet long
\(Area=1456ft^2\)
First, let's look at the given info. We know that there is 155 feet of fence. 155 feet of fence is referring to the entire perimeter. 45.5 feet is referring to only one side length. In a rectangle, however, opposite sides are congruent. The formula for finding the perimeter is 2(l+w).
Let w= width
\(155=2(45.5+w)\) Substitute the values in that we know from given info.
\(155=91+2w\) Distribute the two into the parentheses.
\(64=2w\) Subtract 91 from both sides
\(w=\frac{64}{2}=32\) Divide 2 from both sides to isolate the width.
Although we have found the width, this is not the final answer because the question is asking for the entire area of the fenced area. The formula is A=lw. w=32.5 and l=45.5
\(A=32*45.5=1456ft^2\)Of course, include units in your final answer.
