Question

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

approximately (to the nearest tenth).
The area of the rectangle is 70 cm-.
The width of the rectangle is
cm.
The length of the rectangle is.
cm.​

Answer 1

Part a) Exactly values

The width of the rectangle is
`(√(70))/(2)\ cm`

The length of the rectangle is
`2√(70)\ cm`

Part b) Approximately values

The width of the rectangle is
`4.2\ cm`

The length of the rectangle is
`16.7\ cm`

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

`(70)/(4)=x^2`

square root both sides

`x=(+/-)(√(70))/(2)`

The solution is the positive value

`x=(√(70))/(2)`

therefore

Exactly values

`L=4√(70)}{2}=2√(70)\ cm\\\\W=(√(70))/(2)\ cm`

Approximately values

`L=4√(70)}{2}=16.7\ cm\\\\W=(√(70))/(2)=4.2\ cm`