Answer
$G$
Work Step by Step
Let's figure out the area of the square first so that we know what the area of the rectangle must be.
The area of a square is the square of its side. Let's write out this formula:
$A = s^2$
Let's plug in what we know:
$A = 8^2$
Evaluate the exponent to solve for $A$:
$A = 64$ square inches
We now know that the rectangle also has an area of $64$ square inches.
Let's define some variables:
Let $w$ = the width of the rectangle
Let $4w$ = the length of the rectangle
If we multiply the length and the width of a rectangle together, we will get its area. Let's set up this equation to find the value for the width of the rectangle:
$64 = 4w(w)$
Multiply the right side of the equation:
$4w^2 = 64$
Divide each side of the equation by $4$:
$w^2 = 16$
Take the square root of $16$ to solve for $w$:
$w = -4$ or $w = 4$
We can get rid of the negative value because a length cannot be negative. The width of the rectangle is $4$ inches. However, we need to find the length of the rectangle. Recall that the length of the rectangle is four times the width of the rectangle. Let's set up the equation:
$l = 4w$
Let's plug in our value for $w$:
$l = 4(4)$
Multiply to solve:
$l = 16$
The length of the rectangle is $16$ inches. This corresponds to option $G$.
