The length of a rectangle is less than twice the width, and the area of the rectangle is . Find the dimensions of the rectangle.

Question

The length of a rectangle is 3 yd

 less than twice the width, and the area of the rectangle is 65 yd2

. Find the dimensions of the rectangle.

Answer 1

Let x = width

Then length = 2x - 3

x(2x-3) = 65

2x² - 3x - 65 = 0

(2x - 13)(x + 5) = 0

x = 6.5 or -5

Since x is the width, x can't be negative.

So, width = 6.5 yards and length = 10 yards

Answer 2

Aiden, thanks for coming to us for help!

Let's remember that the Area of a rectangle is A = L x W where L is length, and W is width.

If the Length is 3 yards less that twice the width, we can write the Length as : L = 2W - 3.

Using the equation for Area, we can substitute our new Length formula in as:

Area = L x W = (2W -3) X W = 65 yd²

Here we know that we end up with:

2W²-3W = 65

In the form of a quadratic function this becomes: 2W²-3W-65 = 0. Applying the quadratic formula will give you two answers, W = -5 yd and W = 6.5 yd. Obviously, we won't use the negative value.

This W = 6.5 yards. When plugging this value into the formula for L = 2 (6.5) - 3 = 13 - 3 = 10 yards.

Width = 6.5 yards

Length = 10 Yards