SOLUTION: The area of a rectangle is 5+ sqrt 3. One side is 2+ sqrt 3, what is the lenght of the other side.

Question 624966: The area of a rectangle is 5+ sqrt 3. One side is 2+ sqrt 3, what is the lenght of the other side.
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
If the problem had given you simpler numbers would you be able to figure this out? For example, if the area was 24 and one side was 4, would you be able to figure this out? I would hope that you would know that since A=l*w in a rectangle that you could divide the area by one side (Width) to find other side (length): 24/4 = 6

Now that we know what we would do with simple number, just do the same thing with the numbers you were given! (This can be a very helpful technique with word problems where the numbers are "weird" in some way (square roots, fractions, variable expressions, etc.) Pretend the numebrs are simple and figure our what you would do with them. And then do the same thing with the actual numbers you were given!)

Dividing the given area by the given side:

Now we just simplify this expression. Part of simplifying expressions with square roots in denominators, is to rationalize the denominators. Our denominator has two terms in it: 2 and . Rationalizing two-term denominators takes advantage of the fact that . The left side is a product of two-term expressions. The right side is an expression of perfect squares. So is shows us how to turn any two-term expression into an expression of perfect squares. Since our denominator is a sum, we will look at it as the (a+b) with "a" being 2 and "b" being . The equation above tells us to get perfect squares we need to multiply an (a+b) by an (a-b). So we multiply the numerator and denominator of our fraction by :

We already knwo how the denominators multiply. We get . In the numerators we need to use FOIL to multiply:

which simplifies as follows:

This (or ) is the length.
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