Question

Dana wants to build a rectangular pen for her goats. The length of the pen should be at least 50 feet, and the perimeter of the pen should be no more than 190 feet.Dana’s goat pen could be____ feet wide and _____ feet longHow many different sets of dimensions are possible for this situation?

Answer 1

Step-by-step explanation:

We start by assigning variables to the unknown

Let us call the length x and the width y

From the question, length is at least 50 ft

Thus,we have it that:

`x\ge\text{ 50}`

We apply the formula for the perimeter to compute its lentth as follows:

`\begin{gathered} 2(x\text{ + y)}\leq\text{ 190} \\ x\text{ + y}\leq\text{ 95} \end{gathered}`

We now proceed to make a plot of these two inequalities

We have the attachment as follows:

Now, at what points do we have our answers?

We can notice two distinct lines

Black and Purple. The point of overlap is where we have our answer

Also,we will not consider the points below the x-axis as the measurement of length cannot be negative

Let us pick out the points now

His goat pen could be 40 feet wide and 50 feet long

We can have others like 30 ft wide , 50 feet long