Answer:
(a) 4 units
Explanation:
You want to know the width of a rectangle if its area is 40 square units and its length is 2 units more than twice its width.
Test
It is convenient to test the answers to see which one works:
4(2·4 +2) = 40 . . . . . . . . a width of 4 units works, choice A
5(2·5 +2) = 60
10(2·10 +2) = 220
12(2·12 +2) = 312
Solve (1)
We could solve the quadratic for w:
w(w +1) = 20 . . . . . . . divide by 2
At this point, we can look for factors of 20 that differ by 1:
20 = 1·20 = 2·10 = 4·5
The values of w and (w+1) we are looking for are w=4 and (w+1)=5.
The width is 4 units, choice A.
Solve (2)
Or we could solve using "completing the square".
w² +w = 20 . . . . . . . . . eliminate the parentheses
w² +w +1/4 = 20.25 . . . . . add 1/4 to complete the square
(w +1/2)² = 20.25 . . . . . . write as a square
w +0.5 = √20.25 = 4.5 . . . . take the positive square root
w = 4.5 -0.5 = 4 . . . . . . subtract 0.5
The width is 4 units, choice A.
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Additional comment
Perhaps you can see that we favor the "test" solution, as it is pretty easy to check the answer choices in the given equation.
Yet another easy solution method is writing the equation in the form f(x)=0, and looking for the x-intercepts. The attached graph shows the parabola x(2x+2)-40 and the value of x that makes that zero. A graphing calculator does this pretty easily.
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