Answer
Width $=10\;ft$.
Length $=25\;ft$.
Work Step by Step
Let the width of the deck be $x$.
The length of the deck is $2x+5$.
Area of the deck $=(x)(2x+5)$.
The given area of the deck is $=250\;ft^2$.
Equate both areas.
$\Rightarrow (x)(2x+5)=250$.
Clear the parentheses.
$\Rightarrow 2x^2+5x=250$.
Subtract $250$ from both sides.
$\Rightarrow 2x^2+5x-250=250-250$
Simplify.
$\Rightarrow 2x^2+5x-250=0$
Rewrite the middle term $5x$ as $25x-20x$.
$\Rightarrow 2x^2+25x-20x-250=0$
Factor out the common terms.
$\Rightarrow x(2x+25)-10(2x+25)=0$
Factor out $(2x+25)$.
$\Rightarrow (2x+25)(x-10)=0$
Use the zero product property.
$ 2x+25=0$ or $x-10=0$
Solve for $x$.
$ x=\frac{-25}{2}$ or $x=10$
Width of the deck: $10\;ft$
Length of the deck: $2x+5=2(10)+5=20+5=25\;ft$.
