Answer:
The length is 9 ft and the width is 2 ft
Step-by-step explanation:
Rectangle:
Has two dimensions: Length(l) and width(w)
The area is: A = l*w
In this question:
A = 18.
The length of rectangular garden is 7 feet longer than the width.
This means that l = 7 + w.
So
[tex]A = l*w[/tex]
[tex]18 = (7+w)*w[/tex]
[tex]18 = 7w + w^{2}[/tex]
[tex]w^{2} + 7w - 18 = 0[/tex]
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]\bigtriangleup = b^{2} - 4ac[/tex]
In this question:
[tex]w^{2} + 7w - 18 = 0[/tex]
So [tex]a = 1, b = 7, c = -18[/tex]
Then
[tex]\bigtriangleup = 7^{2} - 4*1*(-18) = 121[/tex]
[tex]w_{1} = \frac{-7 + \sqrt{121}}{2} = 2[/tex]
[tex]w_{2} = \frac{-7 - \sqrt{121}}{2} = -9[/tex]
A dimension cannot be negative, so the width is 2 feet, that is, w = 2.
l = 7 + w = 7 + 2 = 9 ft
The length is 9 ft and the width is 2 ft
