A student has a rectangular backyard with a perimeter of 48 feet. If the width is 10 feet, what is the length of the backyard?

To find the length of the rectangular backyard, we start by using the formula for the perimeter of a rectangle, which is given by:

Perimeter = 2 * (length + width)

In this case, we know the perimeter is 48 feet and the width is 10 feet. We can substitute these values into the formula:

48 = 2 * (length + 10)

Next, we simplify this equation:

48 = 2*length + 20

Subtracting 20 from both sides gives us:

48 - 20 = 2 * length

28 = 2 * length

Now, to isolate the length, we divide both sides by 2:

length = 28 / 2

length = 14 feet

The calculated length of 14 feet corresponds with the option that states 14 feet. Hence, the correct choice for the length of the backyard is indeed 14 feet.

The initial answer provided was incorrect as it listed 16 feet, which does not satisfy the perimeter requirement when substituted back into the equation.