Question

A rectangular parking lot has a perimeter of 820 ft. The area of the parking lot measure SL 42,000 ft

Answer 1

Since the rectangle parking lot has a perimeter of 820ft and the area of the parking lot measures 42,000
`ft^2`, the width of the parking lot is: C. 210 ft.

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(l + w)

Where:

• P represent the perimeter of a rectangle.
• w represent the width of a rectangle.
• l represent the length of a rectangle.

Since this rectangular parking lot has a perimeter of 820 ft, we have:

820 = 2(l + w)

410 = l + w

l = 410 - w

For the area of this rectangular parking, we have:

Area = lw

42000 = lw

42000 = w(410 - w)

`42000=410w-w^2\\\\w^2-410w+42000=0\\\\w^2-200w -210w+42000=0\\\\(w-200)(w-210)=0`

w = 200 feet or w = 210 feet.

Complete Question:

A rectangle parking lot has a perimeter of 820ft. The area of the parking lot measures 42,000
`ft^2`. What is the width of the parking lot?

A. 120 ft

B. 205 ft

C. 210 ft

D. 375 ft

Answer 2

a= 200

b = 210

Explanation:

My assumption is, we have to find the length of sides of rectangle

Given

perimeter = 2a + 2b = 820 ft (i) (here a is smaller side and b is larger side)

area = a*b = 42,000 ft^2 (ii)

from eq (1)

2a + 2b = 820

=> 2(a+b) = 820

=> a+b = 820/2

=> a + b = 410

=> a = 410-b (iii)

putting the value of a in eq(ii), we get

(410-b) *b = 42,000

410b - b^2 = 42,000

0 = b^2 - 410b + 42000

b^2 - 410b + 42000 = 0

b^2- 200b- 210b + 42000 = 0

b(b-200)-210(b-200) = 0

(b-200)(b-210) = 0

or

b= 210 and b = 200

if b is larger side than b =210

By putting value of b in eq(iii),

a = 410 -210 = 200