Question

You have 24 feet of fencing that you are using to make a rectangular dog pen. You want the dog pen to enclose 150 square feet. Is it possible for the 24 feet of fencing to enclose a rectangular area of 150 square feet? Explain.

Answer 1

Not possible

Explanation:

Given that

The area of the pen is 150 ft²

Assuming that the length of the pen is x, then the breadth of the pen will be 24 - x

Area = length * breadth

Area = x (24 - x)

Area = 24x - x²

24x - x² = 150

x² - 24x + 150 = 0

Using general quadratic formula, we have

[-b ± √(b² - 4ac)]/ 2a

Where

a = 1

b = -24

c = 150

On solving the equation, we get a number in the complex form of "i", and not a real number. As such, it's not possible for the 24 feet to enclose the area