SOLUTION: I am helping my daughter do her homework and we are stuck on this, please help me explain it to her. The length of a rectangle is 1cm less than four times its width. If the are

Question 862076: I am helping my daughter do her homework and we are stuck on this, please help me explain it to her.
The length of a rectangle is 1cm less than four times its width. If the area of the rectangle is 39cm (squared), what is the width and the length of the rectangle.
Many thanks,
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
w for width
L for length
k = how much is length than the width; .
m = a factor applied to the width as part of description. Usually this is a natural number.
A = area of rectangegle
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The only unknown variables are L and w.
You are given that k=1, m=4, A=39.

, the first sentence in the description.
, the second sentence in description.

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Values given may often be chosen to make the resulting quadratic equation to be factorable. This will make the solution for w easily found. In "Introductory Algebra", you can usually depend on this factorability; after that, you cannot always depend on this factorability and will need to use general solution of a quadratic equation. Is this example factorable?

If not, or even if it is,

, choosing the form with the positive square root, because we know w must be positive.

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