Respuesta :
Answer:
It didn't saying anything about rounding but the the dimensions in there exact form are:
[tex]L=\frac{-5+\sqrt{249}}{2} \text{ cm}[/tex]
and
[tex]W=\frac{5 + \sqrt{249}}{4} \text{ cm }[/tex].
Now if they said to round to the nearest hundredths the dimensions in this rounded form would be:
L=5.39 cm and W=5.19 cm
(Check your question again and see if you meant what you have)
Step-by-step explanation:
L is 5 less than twice W
L = 2W-5
Area of rectangle=L*W
Area is 28 means L*W=28.
I'm going to insert L=2W-5 into L*W=28 giving me
(2W-5)*W=28
Distribute
2W^2-5W=28
Subtract 28 on both sides
2W^2-5W-28=0
a=2
b=-5
c=-28
We are going to use the quadratic formula.
Plug in...
[tex]W=\frac{-b \pm \sqrt{b^2-4ac}}{2a}\\\\W=\frac{5 \pm \sqrt{(-5)^2-4(2)(-28)}}{2(2)}\\\\W=\frac{5 \pm \sqrt{25+224}}{4}\\\\W=\frac{5 \pm \sqrt{249}}{4}[/tex]
W needs to be positive so [tex]W=\frac{5 + \sqrt{249}}{4}[/tex]
And [tex]L=2W-5=2(\frac{5 + \sqrt{249}}{4})-5[/tex]
[tex]L=\frac{5+\sqrt{249}}{2}-5[/tex]
[tex]L=\frac{5+\sqrt{249}}{2}-\frac{10}{2}[/tex]
[tex]L=\frac{-5+\sqrt{249}}{2}[/tex]
Does L*W=28?
Let's check.
[tex]L \cdot W=\frac{-5+\sqrt{249}}{2} \cdot \frac{5 + \sqrt{249}}{4}[/tex]
[tex]L \cdot W=\frac{249-25}{8}[/tex]
In the last step, I was able to do a quick multiplication because I was multiplying conjugates. (a+b)(a-b)=a^2-b^2.
[tex]L \cdot W=\frac{ 224}{8}[/tex]
[tex]L \cdot W=28[/tex]
