Answer: 3.217 & 12.434
Step-by-step explanation:
If we use w to represent the width, the length will be 6 more than 2 times w.
Hence, the length is [tex]2w+6[/tex].
The area of a rectangle would be its length times its width, so let's make an equation to represent it's area.
[tex]A=w(2w+6)[/tex]
We can also substitute 40 in for A as it's given in the question.
[tex]40 = w(2w+6)[/tex]
Distributing w by multiplying it by both terms in the parentheses, we get
[tex]40 = 2w^2+6w[/tex]
We can make the equation simpler by dividing both sides by 2.
[tex]20 = w^2+3w[/tex]
Subtracting both sides by 20 will make the left-hand side 0.
[tex]0=w^2+3w-20[/tex]
Now that we have put this quadratic equation into standard form (ax²+bx+c), we can find its solutions using the quadratic formula.
For reference, the quadratic formula is
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
In this case, a is 1, b is 3, and c is -20.
Substituting, we get
[tex]w=\frac{-3\pm\sqrt{3^2-4(1)(-20)}}{2(1)}[/tex]
[tex]w= \frac{-3\pm\sqrt{9+80}}{2}[/tex]
[tex]w=\frac{-3+\sqrt{89}}{2}\hspace{0.1cm}or\hspace{0.1cm}\frac{-3-\sqrt{89}}{2}[/tex]
Since the second solution results in a negative number, it cannot be the length of w.
[tex]w=\frac{-3+\sqrt{89}}{2}\approx3.217[/tex]
The width/breadth of the rectangle is 3.217 cm.
To calculate the length, let's substitute the width into the expression for the length:
[tex]l=2(3.217)+6[/tex]
[tex]l=12.434[/tex]
The length of this rectangle is 12.434 cm.
