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?

Question

asked Dec 9, 2020 66.2k views

1 Answer

Hallgeir Engen · Answer 1 · 2020-12-14T14:30:58+0000

Answer:

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

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

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