Answer
Length = $8$ inches
Width = $5$ inches
Work Step by Step
We can make the width of the rectangle equal $x$ as it is unknown, and as the length is 3 in. longer, it can be expressed as $(x+3)$.
So, now we know;
Length = $x+3$
Width = $x$
Area = $40$ $in^2$
We also know that the formula for the area of a rectangle is; $Length \times Width$.
We can substitute the values found earlier into this formula to form a quadratic equation!
Area = Length $\times$ Width
$40 = (x+3) \times x$
$40 = x^2+3x$
Subtract 40 from each side to make the equation equal 0.
$x^2+3x-40=0$
We can now solve this quadratic equation by factoring!
$x^2+3x-40=0$
$x^2+8x-5x-40=0$
$x(x+8)-5(x+8)=0$
$(x-5)(x+8)=0$
To find the solutions for $x$, we can make each bracket = 0.
$(x-5) = 0$ or $(x+8)=0$
$x=5$ or $x=-8$
$x$ can't be a negative number because we are looking for the width of a rectangle, which cannot be below $0$. So, $x=5$
Length = $(5)+3$
=$8$ inches
Width = $5$ inches
