Question

A college parking lot is 140 ft long and 90 ft wide. The college wants to increase the area of the lot by 29% by adding strips of equal width to one end and one side. (So, the new shape will be a larger rectangle.) Find the width of one such strip. Round your answer to the nearest integer.

Answer 1

To find the width of one strip added to the parking lot, we need to find the increase in area and divide it by the length of the parking lot. By setting up and solving an equation, we determine that the width of one strip is approximately 15 feet.

Step-by-step explanation:

To find the width of one strip, we need to find the increase in area and divide it by the length of the parking lot. The increase in area is given as 29% of the original area. The original area of the parking lot is the product of its length and width: 140 ft * 90 ft = 12600 sq ft. The increase in area is 29% of this, which is (29/100) * 12600 sq ft = 3654 sq ft.

We need to add strips to one end and one side of the lot, so the length of the new parking lot will be increased by the width of the strip, and the width will be increased by the width of the strip as well. Let's say the width of the strip is 'w' feet. So, the new dimensions of the parking lot will be (140 + w) ft and (90 + w) ft.

The increase in area is equal to the area of the strip, which is the product of its width and the increase in length or width of the parking lot. Using this information, we can set up the equation:

(140 + w)(90 + w) - 12600 = 3654

Expanding and simplifying this equation, we get:

12600 + 140w + 90w + w^2 - 12600 = 3654

Simplifying further, we get:

230w + w^2 = 3654

Now, we can rearrange the equation to solve for 'w':

w^2 + 230w - 3654 = 0

This is a quadratic equation, which can be solved by factoring or using the quadratic formula. After solving, we get two possible values for 'w', one of which is negative and one of which is positive. Since the width cannot be negative, we take the positive value as the width of one strip.

Rounding this value to the nearest integer, we find that the width of one strip is approximately 15 feet.

Answer 2

The initial dimenssions of the park lot are:

length: 140 ft
width: 90 ft

initial area: 140 * 90 = 12,600 ft^2

Area increased 29% = 12,600 * 1.29 = 16,254 ft^2

width of the strips: x

New length: 140 + x

New width: 90 + x

New area: (140+x)(90+x) = 16,254

Solution of the equation:

12600 + 230x + x^2 = 16254

=> x^2 + 230x - 3654 = 0

Use the quadratic formula.

x = {-230 +/- √[ 230^2 - 4*1*(-3654) ]} / 2 =

x = 14.92

The other solution is negative so it is discarded.

Answer: 15 ft