Question

A building with length 44ft and width 66ft is to have a walkway with a length of xft such that the area of the building is the same as the area of the walkway. What is the length of x ?

Answer 1

To find the length of the walkway, set up an equation with the areas of the building and walkway. Solve the equation using the quadratic formula. The length of the walkway is 20 ft.

Step-by-step explanation:

To find the length of the walkway, we need to set up an equation where the area of the building is equal to the area of the walkway. The area of a rectangle is found by multiplying its length and width. So we have:

44 ft × 66 ft = (44 ft + x ft) × (66 ft + x ft)

Now we can solve this equation to find the value of x.

4814 ft² = (44 ft + x ft) × (66 ft + x ft)

4814 = (44 + x)(66 + x)

4814 = 2904 + 110x + x²

x² + 110x + 2904 - 4814 = 0

x² + 110x - 1910 = 0

Using the quadratic formula, we find that x = -95 or x = 20.

Since the length of the walkway cannot be negative, the length of x is 20 ft.