Question

John is building a rectangular puppy kernel up against his house using 31 feet of fencing. The side against the houses does not need a fence and the side parallel to his house needs to be 15 feet long. Write an equation that models the situation and solve for the length of one of the shorter that extends out from the house.

Answer 1

Hint: Now we are given that one side of the fencing is 15 feet. Since opposite sides of the rectangle are equal we can say that the other two sides of fencing will be equal. Let the other side be x feet. Now we will form an equation by calculating the total perimeter of the 3 sided fence and equating it to the total fencing available.

Complete step by step solution:
Now we are given that John is building a rectangular puppy kernel.
The total fencing that he has is 31 feet.
We are given that the side against the house does not need a fence. The side parallel to his house needs to be 15 feet long.
Hence we have that the fence is 3 sided fence with one of its sides as 15 feet.
Now we know that the opposite sides of the rectangle are equal.
Let the other two sides of the fence be x.
Hence we get the perimeter of the fence is x + x + 15.
Now we have that the total fence available is 31 feet.
Hence we get the equation as, x + x + 15 = 31.
Now let us subtract 15 from both sides of the equation. Hence we get,
\[\begin{align}
  & \Rightarrow x+x+15-15=31-15 \\
 & \Rightarrow 2x=16 \\
\end{align}\]
Now let us divide the above equation by 2. Hence we get x = 8.
Hence the smaller side of the fence must be of 8 feet.

Note: Now note that the perimeter of the rectangle is given by $2\left( l+b \right)$ where l is length and b is breadth of rectangle. But since we want to fence on just 3 sides we will not use this formula to find the total fencing.