Question

A rectangular porch has dimensions of (2x+3) feet and (x+9) feet. the area of the porch is 500 square feet. what are the length and width of the porch?

Answer 1

The dimensions of the porch are
`25\ ft` by
`20\ ft`

Explanation:

we know that

The area of the porch is equal to the length multiplied by the width

`A=(2x+3)(x+9)`

`A=500\ ft^(2)`

so

`500=(2x+3)(x+9)`

Solve for x

`500=2x^(2) +18x+3x+27\\ \\2x^(2) +21x-473=0`

Solve the quadratic equation by graphing

The solution is
`x=11\ ft`

see the attached figure

The dimensions are

`(2x+3)=2(11)+3=25\ ft`

`(x+9)=11+9=20\ ft`