Answer
Length = $12$ ft
Width = $7$ ft
Work Step by Step
We know that the 2 sides of the rectangle are $(x+5)$ and $x$, and the area of the rectangle is $84$ $ft^{2}$.
The formula for finding the area of a rectangle is; Length $\times$ width.
We know that;
Length = $(x+5)$
Width = $x$
So, we can substitute these values into the formula and form a quadratic equation!
Area = Length x Width
$84 = (x+5)\times x$
$84 = x^{2} +5x$
Subtract 84 from both sides of the equation.
$x^{2} +5x-84=0$
Now, we have a quadratic equation. We can solve this equation to find the solution for $x$ by factorizing.
$x^{2} +5x-84=0$
$x^{2} +12x-7x-84=0$
$x(x+12)-7(x+12)=0$
$(x-7)(x+12)=0$
Now, we can get the roots of the equation by making each bracket equal to 0.
$(x-7)=0$ or $(x+12)=0$
$x=7$ or $x=-12$
We cross out $-12$, as a rectangle cannot have a negative value as one of its sides, so $x$=7.
Length= $(7)+5$
= $12$ ft
Width = $7$ ft
