Question

A rectangular vegetable garden will have a width that is 2 feet less than the length, and an area of 48 square feet. If x represents the length, then the length can be found by solving the equation: x(x−2)=48 x(x-2)=48 What is the length, x, of the garden? The length is _____ feet.

Answer 1

The length is 8 feet 

Answer 2

The length is
`8` feet.

Explanation:

we know that

the area of the rectangle is equal to

`A=xy`

where

x is the length side of rectangle

y is the width side of rectangle

In this problem we have

`A=48\ ft^(2)`

so

`48=xy` ----> equation A

`y=x-2` ------> equation B

substitute equation B in equation A

`48=x(x-2)`

`x^(2)-2x-48=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

`x^(2)-2x-48=0`

so

`a=1\\b=-2\\c=-48`

substitute in the formula

`x=\frac{-(-2)(+/-)\sqrt{-2^(2)-4(1)(-48)}} {2(1)}`

`x=\frac{2(+/-)√(4+192)} {2}`

`x=\frac{2(+/-)14} {2}`

`x=\frac{2+14} {2}=8\ ft` -----> the solution

`x=\frac{2-14} {2}=-6`