Question

Area = 300 square feet

Length must be 12 feet longer than width
Find the dimension of the pen

Answer 1

`Length=24.32` feet

`width=12.32` feet

Explanation:

Let x be the width of a rectangle

Let l be the length of a rectangle

Let A be the area of rectangle

Given.

Length must be 12 feet longer than width

therefore

`Length=12+w`

`l=12+w`

Area of rectangle

`A=300`

We know that area of rectangle is

`A=l* w`---------------------(1)

put all known values in equation 1

`300=(12+x)* x`

`x^(2) +12x=300\\x^(2) +12x-300=0`

Find roots by this formula

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

`=\frac{-12\pm\sqrt{12^(2)-4(1)(-300)}}{2(1)}`

`=(-12\pm√(1344))/(2)`

`x=-6+4√(21) \\x=-6-4√(21)`

`x=12.32\\x=-24.32`

check both value in equation 1

for
`x=12.32`

`A=(12+12.32)* 12.32`

`A=299.62`

`x=12.32` is satisfy the equation

So The length of rectangle
`l=12+12.32`=24.32 feet

And width is 12.32 feet