Answer:
The width is 5 inches.
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.