Question

A medical office has a rectangular parking lot that measures 120 ft by 200 ft. The owner wants to expand the size of the parking lot by adding an equal distance to two sides as shown. If zoning restrictions limit the total size of the parking lot to 35,000 ft^2. What range of distances can be added?

Answer 1

Answer:

$x\leq 31.3 ft$

Step-by-step explanation:

It is given that the parking lot measures 120 ft by 200 ft. The owner wants to expand the size of parking lot by adding equal distance to two sides.

Let's assume that he added 'x' ft on both the sides, then the area after the addition must be less than 35000 square feet. So we have,

$(x+120)(x+200)\leq 35000$

Solving for 'x' we get,

$x^2+320x-11000\leq 0$

Now we can use quadratic formula to find the roots of the equation, we can use,

$x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$

In our equation, b= 320, a = 1 and c = -11000, putting the values we get,

$x\leq 10\sqrt{(366)-16}$

$x \leq  31.3 ft$

Here we have ignored the negative root of 'x' because length cannot be negative.

Therefore, the range of distance that be added should be less than 31.3 ft.