Answer
Length = $24$ ft
Width = $15$ ft
Work Step by Step
First, we can illustrate the problem given in the question for a better understanding, as seen below.
We know that;
Length = $(x+9)$
Width = $x$
Area = $360 ft^2$
The formula for the area of a rectangle is; Length $\times$ Width.
We can use the values we have and substitute them into this formula to form a quadratic equation.
Area = Length $\times$ Width
360 = $(x+9) \times x$
$360 = x^2+9x$ (Subtract 360 from the equation to make it equal 0)
$x^2+9x-360=0$
We now have our quadratic equation, which we can solve by factoring!
$x^2+9x-360=0$
$x^2+24x-15x-360=0$
$x(x+24)-15(x+24)=0$
$(x-15)(x+24)=0$
To find the solutions for $x$, we can make both brackets = 0.
$(x-15)=0$ or $(x+24)=0$
$x=15$ or $x=-24$
We rule out $-24$, as $x$ cannot be a negative number in this case as it is the width of the rectangle, which cannot be lower than $0$. So, $x=15$
Length = $(15)+9$
=$24$ ft
Width = $15$ ft
