Answer:
Part a) Exactly values
The width of the rectangle is [tex]\frac{\sqrt{70}}{2}\ cm[/tex]
The length of the rectangle is [tex]2\sqrt{70}\ cm[/tex]
Part b) Approximately values
The width of the rectangle is [tex]4.2\ cm[/tex]
The length of the rectangle is [tex]16.7\ cm[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
The area of rectangle is equal to
[tex]A=LW[/tex]
we have
[tex]L=4x\ cm\\W=x\ cm[/tex]
substitute the values in the formula
[tex]A=4x(x)[/tex]
[tex]A=4x^2[/tex]
[tex]A=70\ cm^2[/tex]
so
[tex]70=4x^2[/tex]
Solve for x
Divide by 4 both sides
[tex]\frac{70}{4}=x^2[/tex]
square root both sides
[tex]x=(+/-)\frac{\sqrt{70}}{2}[/tex]
The solution is the positive value
[tex]x=\frac{\sqrt{70}}{2}[/tex]
therefore
Exactly values
[tex]L=4\sqrt{70}}{2}=2\sqrt{70}\ cm\\\\W=\frac{\sqrt{70}}{2}\ cm[/tex]
Approximately values
[tex]L=4\sqrt{70}}{2}=16.7\ cm\\\\W=\frac{\sqrt{70}}{2}=4.2\ cm[/tex]
