A retangular pen for a pet is 5 feet longer than it is wide. Give possible values for the width. W of the pen if its area must be between 176 and 750 square feet inclusively. The width of the pen ranges from the smaller value of the width, Feet to the larger value of width feet inclusively.
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What formula would you use to figure out this word problem?
A rectangular pen for a pet is 8 feet longer than it is wide. Give possible values for the width W of the pen if its area must be between 180 and 825 square feet, inclusively.
To find the possible values for the width, we can start by setting up an equation based on the information given. Let's assume that the width of the rectangular pen is denoted by "W" in feet.
Given that the length of the pen is 5 feet longer than the width, we can represent the length as "W + 5" feet.
The area of a rectangle is calculated by multiplying its length and width. Therefore, the area of the pen is:
Area = Width * Length
Area = W * (W + 5)
Area = W² + 5W
According to the problem, the area must be between 176 and 750 square feet inclusively. This gives us the following inequality:
176 ≤ W² + 5W ≤ 750
To find the possible values for the width (W), we can solve this inequality.
First, we simplify the inequality by subtracting 176 from each side:
0 ≤ W² + 5W – 176 ≤ 574
Now, let's solve the quadratic equation W² + 5W – 176 = 0:
To find the roots of the equation, we can use factoring, completing the square, or the quadratic formula.
Factoring the equation gives us:
(W + 16)(W – 11) = 0
Setting each factor equal to zero, we find two possible values for W:
W + 16 = 0 or W – 11 = 0
W = -16 or W = 11
Since the width cannot be negative for a physical pen, we can disregard W = -16.
Therefore, the possible values for the width (W) of the pen are W = 11 feet.
In conclusion, the width of the rectangular pen must be 11 feet.