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

The width is 5 inches.

Step-by-step explanation:

From the question, the length of a rectangle is 3 inches more than twice its width, we are to find its width if its area is 65 square inches.

To find the width, we will follow the steps below;

First, we will need to write the equation for the problem and then solve

Let l = length of the rectangle

     w = width of the rectangle

We can now proceed to write the statements of the question mathematically

"The length of a rectangle is 3 inches more than twice its width" can be written mathematically as l = 3 + 2w (1)

"its area is 65 square inches" implies that

Area of the rectangle = 65 square inches.

But recall that;

Area  of a rectangle = l×w

              65  =   l × w  (2)

We now have two system of linear equation, we are going to use substitution method to solve.

substitute equation(1) into equation (2)

65 = (3 + 2w)w

65 = 3w + 2w²

The equation can be re-arrange

2w²+ 3w - 65 = 0  (3)

This is a quadratic equation, we will solve using factorization method.

65×2 = 130

find to numbers such that its product gives -130 and its sum gives 3

The numbers are -10 and 13

-10 × 13 = -130

-10 + 13 = 3

We are going t0 replace 3w by (13w - 10w)

Equation (3) becomes;

2w²+13w -10w- 65 = 0

We can now proceed to factorize

(2w²+13w) (-10w- 65) = 0

In the first parenthesis, we are going to factor out w while in the second parenthesis we will factor out -5

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

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

Either  w- 5 = 0      or         2w + 13 = 0

Either  w= 5            or  2w= -13

Either  w = 5         or w= -13/2

But there is no negative length, so   w= 5

Therefore the width is 5 inches.

could you reply to this with the question so i can ?