Question

Determine the lengths of the sides of the rectangle using the given area. Give answers both exactly and

Answer 1

Answer:

Part a) Exactly values

The width of the rectangle is $\frac{\sqrt{70}}{2}\ cm$

The length of the rectangle is $2\sqrt{70}\ cm$

Part b) Approximately values

The width of the rectangle is $4.2\ cm$

The length of the rectangle is $16.7\ cm$

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The area of rectangle is equal to

$A=LW$

we have

$L=4x\ cm\\W=x\ cm$

substitute the values in the formula

$A=4x(x)$

$A=4x^2$

$A=70\ cm^2$

so

$70=4x^2$

Solve for x

Divide by 4 both sides

$\frac{70}{4}=x^2$

square root both sides

$x=(+/-)\frac{\sqrt{70}}{2}$

The solution is the positive value

$x=\frac{\sqrt{70}}{2}$

therefore

Exactly values

$L=4\sqrt{70}}{2}=2\sqrt{70}\ cm\\\\W=\frac{\sqrt{70}}{2}\ cm$

Approximately values

$L=4\sqrt{70}}{2}=16.7\ cm\\\\W=\frac{\sqrt{70}}{2}=4.2\ cm$