Question

If the area of a rectangle is 10in^2, the length (2+sqrt(2))in. What is the width?

Answer 1

area=length times width
area=10
length=2+√2
width=w

10=(2+√2)(w)
divide both sides by (2+√2)

`(10)/(2+ √(2) ) =w`
if we were to rationalize the dnomenator
multiply by
`(2- √(2) )/(2- √(2) )`

`(10(2- √(2)))/(4-2 ) =w`

`(20- 10√(2))/(2) =w`

`10- 5√(2) =w`

the width is 10-5√2 m