The area of a rectangle is 48 square inches. The length is three times the width. What is the length?

Answer 1

Area of a rectangle is length X width, or lw.

Let l = length of rectangle

w = width of rectangle

A = area of rectangle = 48 in²

We have 2 unknowns, length and width, so we need 2 equations to solve for this:

Eq. I: lw = 48

Eq. II: l = 3w

Using the value of l in terms of w from Eq. II in Eq. I we can solve for w:

lw = 48 Eq. I

(3w)w = 48 substituting for l

3w² = 48 simplify

w² = 48/3 divide both sides by 3

w² = 16 simplify

w =±4 square root both sides

Because width and length have to be positive measurements, we get w = +4 inches. Plug this value for w into Eq. II we can solve for the length directly:

l = 3w Eq. II

l = 3(4) substitute for w

l = 12 solve for l

Therefore, the length of the rectangle is 12 inches.

Answer 2

Area of a rectangle is length times width, or

A = l * w

Substitute in what you know, and solve for the length.

A = 48

l = 3 * w

So

48=(3 * w) * w

48 = 3 w²

Divide both sides by 3

16 = w²

Square root both sides

4 = w

The width is 4, and the length is three times the width, so 3 * 4 = 12

The length is 12 inches.