Mastering College Algebra: Unlocking the Length of a Rectangle

Have you ever found yourself scratching your head over a simple geometry problem during exam prep? Trust me, it happens more often than you'd think! Let’s delve into a classic rectangle problem that’s often seen in College Algebra—and yes, it’s one that could pop up on your CLEP practice exam.

A Rectangle with a Twist

Here’s the problem: The length of a rectangle is 4 times its width. If its width is 8, what’s its length? Sounds easy, right? But before you rush to the answer, let’s take a moment to break it down. Remember: algebra isn’t just about getting to an answer; it’s about understanding the how and why behind it.

Understanding the Components

We know that in any rectangle, the length can be calculated by multiplying its width by a given factor. In this case, the problem states that the length is 4 times the width. So, if our width is 8, can you guess how we find the length? That’s right—by multiplying!

The math goes like this:
[ \text{Length} = \text{Width} \times 4 ]
[ \text{Length} = 8 \times 4 ]
[ \text{Length} = 32 ]

Did you see that progression? The correct answer is 32, as given in option D.

Analyzing the Wrong Choices

Now, let’s look at the other options and see why they don’t make the cut:

• Option A (12): This would only give us a length that is 1.5 times the width. Not exactly what we need, right?
• Option B (4): This option suggests the length is the same as the width. Not happening!
• Option C (16): While it might feel close, this length only doubles the width—definitely not consistent with the “4 times” rule.

You see, every choice has its reasoning, and understanding that can help you confidently avoid mistakes.

Wrapping Up

So, if you’re sitting down with your notes for the College Algebra CLEP exam, remember this: it’s crucial to grasp the reasoning behind formulas and operations. Don’t just memorize—understand! Now, go ahead and tackle more problems like this one. With practice and confidence, you’ll be ready to conquer that exam.

In conclusion, when tackling problems about geometry on the College Algebra CLEP exam, always start with what you know. Numbers tell a story; it's just up to you to read them. Happy studying!