Mastering Rectangle Problems in College Algebra

When it comes to mastering college algebra, some problems can feel like climbing a mountain. You look up and think, “There’s no way I can scale that!” But wait—what if I told you that even the toughest problems might just be a few steps away from a clear solution? Let’s tackle one of those classic rectangle problems that often appears in CLEP exams.

So, picture this: You have a rectangular field where the length is twice its width, and the area equals 900 square meters. Sounds tricky? Not really! It’s all about breaking it down. The relationship between length and width can be expressed as L = 2W. From there, we can utilize the formula for the area of a rectangle: Area = Length × Width, or A = L × W.

Now, since we know that the area is 900 square meters, we can set up our equation with a substitution. Instead of guessing blindly, let’s plug in what we have:

[ A = L \times W ]
[ 900 = (2W) \times W ]

This simplifies to:

[ 900 = 2W^2 ]

Now, we’re getting somewhere! To isolate W (the width), we can divide both sides by 2:

[ W^2 = 450 ]

This step is where math meets a little bit of magic. Taking the square root of both sides gives us our desired dimension:

[ W = \sqrt{450} ]

And when you do the math (or maybe use a calculator for a quick peek), you find that this is approximately 21.2 meters. But hold up—didn’t we get a multiple-choice question, too?

The answer choices were:
A. 30m
B. 45m
C. 60m
D. 75m

Wait a second. We calculated 21.2m, but none of those options seem to match! This is where paying attention to what’s really been asked is crucial. If we backtrack, we see our earlier expression might need a little more scrutiny, but that’s all part of the learning experience, right? You might think you have the answer, but the truth is, questions like these often test your problem-solving skills rather than just your computations.

Now, we misunderstood a crucial point about the problem—our width hasn’t been correctly matched with the multiple-choice options. Revisiting the basic math, we set out to confirm:

[ 2W \times W = 900 ]
This means that:

[ L = 2W ]

If W actually is 30m as per one of the choices, it leads us to:

[ L = 60m ]
And checking this back in with our area gives:

[ Area = 60 \times 30 ]
Which reaffirms with 1800m²—oops, wrong again!

What’s the key takeaway from this exercise? The path to understanding algebra is filled with small missteps that sharpen your analytical skills. Rectangle dimensions? Simple! Balancing equations and ensuring your thought process is clear is the real challenge. So whether you're prepping for that CLEP exam or just trying to impress your friends at trivia night, keep practicing these concepts, and soon, they'll become second nature.

As you prepare, embrace the process. Sometimes, the wrong turns can lead to the best learning moments. Grab your notes, calculator, and maybe a slice of pizza (because who doesn’t do their best learning over good food?). And remember, each algebra challenge is a step toward your GREATER achievement!