Question 2.5.1: The perimeter P of a rectangular livestock pen is 40 feet. I......
The perimeter P of a rectangular livestock pen is 40 feet. If the width w is 6 feet, find the length.
Step 1:
We start by substituting the given values into the formula for the perimeter of a rectangle, which is P = 2l + 2w. In this case, the perimeter is given as 40 feet and the width is given as 6 feet.
Step 2:
We then simplify the equation by multiplying 2 and 6, which gives us 12.
Step 3:
The equation now becomes 40 = 2l + 12.
Step 4:
To solve for l, we need to isolate the variable. We can do this by subtracting 12 from both sides of the equation. This gives us 40 - 12 = 2l.
Step 5:
Simplifying further, we get 28 = 2l.
Step 6:
To find the value of l, we divide both sides of the equation by 2. This gives us l = 14.
Step 7:
Therefore, the length of the rectangular pen must be 14 feet.
Final Answer
First we substitute 40 for P and 6 for w in the formula P=2 l+2 w. Then we solve for l:
\begin{array}{lrl}\text { When } & P & =40 \text { and } w=6 \\\text { the formula } & P & =2 l+2 w \\\text { becomes } & 40 & =2 l+2(6) \\\text { or } & 40 & =2 l+12 \quad \text { Multiply } 2 \text { and } 6\end{array}\begin{array}{ll}28=2 l & \text { Add }-12 \text { to each side } \\14=l & \text { Multiply each side by } \frac{1}{2}\end{array}
To summarize our results, if a rectangular pen has a perimeter of 40 feet and a width of 6 feet, then the length must be 14 feet.
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