Question

A rectangular parking lot has a perimeter of 820 ft. The area of the parking lot measures 42,000 ft2. What is a dimension of the parking lot? 120 ft 205 ft 210 ft 375 ft.

Answer 1

To solve the problem we must know about quadratic equations.

Quadratic Equation

A quadratic equation is an equation that can be written in the form of

ax²+bx+c.

Where a is the leading coefficient, and

c is the constant.

The breadth of the rectangle is 200 ft, while the length is 210 ft.

Explanation

Given to us

• Area of the parking lot = 42,000 ft²
• Perimeter of the parking lot = 820 ft

Area of the parking lot

Area of the parking lot = Area of the rectangle

42,000 ft² = Length x Breadth

Solving for L,

$42,000 = L \times B\\\\ L = \dfrac{42,000}{B}$

Perimeter of the parking lot

Perimeter of the parking lot = Perimeter of the rectangle

820 ft. = 2(Length + Breadth)

820 ft. = 2(L+ B)

$2(L+ B) = 820\\\\ (L+B) = \dfrac{820}{2}\\\\ (L+B) = 410$

Substituting the value of L,

$(L+B) = 410\\\\ (\dfrac{42,000}{B}) +B = 410\\\\ 42000 + B^2 = 410B\\\\ B^2 -410B +42000 = 0$

Quadratic Expression

Solving the quadratic Expression,

$B^2 -410B +42000 = 0\\\\ (B-210)(B-200)=0$

Equation the factors against zero,

B-210=0

B = 210

B-200=0

B = 200

Hence, the breadth of the rectangle is 200ft, while the length is 210 ft.

Learn more about Quadratic Expression:

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