Question

The length of a rectangular flower bed is 2ft longer than the width. If the area is 6ft, then what are the exact length and width?

Answer 1

`w=-1+√(7)\ ft`

`L=1+√(7)\ ft`

Explanation:

we know that

The area of a rectangle is equal to

`A=LW`

In this problem we have

`A=6\ ft^(2)`

so

`6=LW` ------> equation A

`L=W+2` -----> equation B

substitute equation B in equation A

`6=(W+2)W`

`6=W^(2) +2W\\ \\W^(2) +2W-6=0`

The formula to solve a quadratic equation of the form
`ax^(2) +bx+c=0` is equal to

`x=\frac{-b(+/-)\sqrt{b^(2)-4ac}} {2a}`

in this problem we have

`W^(2) +2W-6=0`

so

`a=1\\b=2\\c=-6`

substitute in the formula

`w=\frac{-2(+/-)\sqrt{2^(2)-4(1)(-6)}} {2(1)}`

`w=(-2(+/-)√(28))/(2)`

`w=(-2(+/-)2√(7))/(2)`

`w=(-2(+)2√(7))/(2)=-1+√(7)` ------> the value positive is the solution

`w=(-2(-)2√(7))/(2)=-1-√(7)`

therefore

`w=-1+√(7)\ ft`

Find the value of L

`L=W+2` ------>
`L=-1+√(7)+2=1+√(7)\ ft`