Question 400415
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, <i>not subtract the number from 8</i>, 8-n.<br>
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:
{{{A = 3w^2 - 8w}}}
This is the answer to part a.<br>
To find the area when the width is 10, we just substitute a 10 for w:
{{{A = 3(10)^2 - 8(10)}}}
which simplifies as follows:
A = 3(100) - 8(10)
A = 300 - 80
A = 220 square centimeters.