SOLUTION: The length of a rectangle is 8 centimeters less than 3 times with width. a write a polynomial that represents the area of the rectangle b find the area of the rectangle when the

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Question 400415: The length of a rectangle is 8 centimeters less than 3 times with width.
a write a polynomial that represents the area of the rectangle
b find the area of the rectangle when the width is 10 centimeters.
Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website!
Let w = width. Then, since the length is 8 less than 3 times the width,:
l = 3w - 8
Note how the English "8 less than 3 times the width" is in the opposite order to the expression 3w - 8. This is often the case with subtraction. You have to be careful with these. Just ask your self: "How do I figure out 8 less than a number?" With some thought you should be able to figure out that you subtract 8 from the number, n-8, not subtract the number from 8, 8-n.

Since area of a rectangle is length times width, A = lw, we can use:
A = (3w-8)(w)
for the area of this rectangle. Multiplying out the right side we get:

This is the answer to part a.

To find the area when the width is 10, we just substitute a 10 for w:

which simplifies as follows:
A = 3(100) - 8(10)
A = 300 - 80
A = 220 square centimeters.