Answer:
Width = 15 inches Length = 20 inches
Step-by-step explanation:
The area of a rectangle is calculated using the following formula.
[tex]A = Lx[/tex] (1)
Where L is the length and x is the width of the rectangle
In this case we know that the length of the rectangle is 5 inches greater than its width. This means that:
[tex]L = x + 5[/tex] (2)
Also The area of a rectangle can be represented by the equation [tex]x^2 + 5x = 300[/tex]
so to find the width x we solve the equation
[tex]x^2 + 5x -300=0[/tex] (3)
For an equation of the form [tex]ax ^ 2 + bx + c = 0[/tex] the quadratic formula is:
[tex]x=\frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]
In this case note that:
[tex]a=1\\b=5\\c=-300[/tex]
Then:
[tex]x=\frac{-5\±\sqrt{(5)^2-4(1)(-300)}}{2(1)}[/tex]
[tex]x=\frac{-5\±\sqrt{25+1200}}{2}[/tex]
[tex]x=\frac{-5\±\sqrt{1225}}{2}[/tex]
[tex]x=\frac{-5\±35}{2}[/tex]
[tex]x_1=\frac{-5+35}{2}[/tex] → [tex]x_1=15[/tex]
[tex]x_2=\frac{-5-35}{2}[/tex] → [tex]x_2=-20[/tex]
We take the positive solution [tex]x=15\ in[/tex]
Now we use equation (2) to find L
[tex]L = x + 5[/tex]
[tex]L = 15 + 5[/tex]
[tex]L = 20\ in[/tex]
