Respuesta :
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,
[tex]42,000 = L \times B\\\\ L = \dfrac{42,000}{B}[/tex]
Perimeter of the parking lot
Perimeter of the parking lot = Perimeter of the rectangle
820 ft. = 2(Length + Breadth)
820 ft. = 2(L+ B)
[tex]2(L+ B) = 820\\\\ (L+B) = \dfrac{820}{2}\\\\ (L+B) = 410[/tex]
Substituting the value of L,
[tex](L+B) = 410\\\\ (\dfrac{42,000}{B}) +B = 410\\\\ 42000 + B^2 = 410B\\\\ B^2 -410B +42000 = 0[/tex]
Quadratic Expression
Solving the quadratic Expression,
[tex]B^2 -410B +42000 = 0\\\\ (B-210)(B-200)=0[/tex]
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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