Question

The length of a rectangle is 3 inches more than twice its width, and its area is 65 square inches. What is the width?

If w = the width of the rectangle, which of the following expressions represents the length of the rectangle?

2w + 3
2(w + 3)
3(2w)

Answer 1

Let L be the length of the rectangle and W be its width. Translating the first sentence into mathematical expressions, we get, L=2W+3. To get the area of a rectangle, we will use the formula A=L*W. Since we are already given with the area, we will substitute this value to the formula, together with the expression of L in terms of W. Thus, 65=(2W+3)*(W). Further simplification would yield

65=2W^2+3W
2W^2+3W-65=0

We have a quadratic equation, hence, we will solve for its factors. We have,

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

The two roots of the equation are: -13/2 and 5. Since we can only have positive numbers for dimensions, the width of the rectangle is 5 in.

The expression for the length of the rectangle is 2W+3.