Question

Jefferson High School is looking to expand its student parking lot by expanding the existing lot as

shown below.

Expanded part of lot

75 ft.

Old lot

165 ft.

School

300 ft.

75 ft.

x ft.

The size of the new parking lot will be twice the size of the old parking lot. How many feet, x, was the

old parking lot expanded by?

Answer 1

x = 60 feet

Explanation:

Area of a rectangle = Length * Breadth

School Area = 165 * 300 = 49500 square feet

Area of (school + old lot) = (75+165)*(300+75) = 90000 square feet

Area of old lot = Area of (School + old lot) – Area of school

Area of old lot = 90000-49500 = 40500 square feet

Since size of new packing lot is twice that of the old lot,

Size of the new packing lot = 2 * 40500 = 81000 square feet

Total size of the whole building = 81000 + 49500 = 130500 square feet

To get the value of x,

(300 + 75+ x)*(165 + 75 + x) = 130500

(375+x)*(240 + x) = 130500

x^(2)+615x+90000=130500

x^(2)+615x-40500=0

Solving the quadratic equation above

x-60x+675x-40500=0

(x-60)(x+675)=0

x=60 or x= -675

Since length cannot be negative, x = 60 square feet