Mastering the PERT: Finding the Width of a Swimming Pool

Ever found yourself scratching your head over a question like this? “If the perimeter of a rectangular swimming pool is 30 meters and its width is 3 meters less than its length, what’s the width?” It might sound tricky at first, but trust me, breaking it down will not only make it clearer but also help boost your confidence for the Postsecondary Education Readiness Test (PERT)!

Let’s start with something simple—the formula for the perimeter of a rectangle. It’s given by ( P = 2L + 2W ), where ( L ) is the length and ( W ) is the width. So, if you know the perimeter and have a bit of information about the dimensions, you’re already halfway there!

In your problem, the perimeter is 30 meters. We also know that the width is 3 meters less than the length. Let’s turn those words into equations and see where they lead us.

The first equation we set up is based on the perimeter: [ 2L + 2W = 30 ]

Now, for the second equation, remember that the width (W) is 3 meters less than the length (L). So, we can express this as: [ W = L - 3 ]

With these two equations in hand, let’s plug the second equation into the first. This means we’re substituting for W, which helps us simplify our work. Grab a pencil; here’s the magic:

1. Substitute ( W ) in the perimeter equation: [ 2L + 2(L - 3) = 30 ]

2. Simplifying this, we can combine like terms: [ 2L + 2L - 6 = 30 ] [ 4L - 6 = 30 ]

3. Now, let’s add 6 to both sides: [ 4L = 36 ]

4. Finally, divide by 4 to solve for L: [ L = 9 ]

Great! We've found the length. But hold up, we need the width, right? Remember the second equation we set up? Let's go back to that—( W = L - 3 ). So if ( L = 9 ), we substitute to find: [ W = 9 - 3 = 6 ]

Bingo! The width of the pool is 6 meters. Now, doesn’t it feel good to have wrapped your head around that?

This kind of problem is a perfect example of what you might expect on the PERT, where applying formulas and solving for variables is key. Whether you’re prepping for this test or just brushing up on your math skills, understanding how to manipulate equations like these can really ballpark your confidence.

Math problems don't have to be daunting! Whether it's calculating the width of a rectangular pool or solving algebraic equations, practice makes perfect. So, do yourself a favor: take time to work through similar PERT practice problems. You’ll not only gain the knowledge needed for the exam but also build a foundation for your future studies.

And hey, speaking of swimming pools, isn’t it fascinating how geometry pops up everywhere in our lives? From planning a backyard pool to understanding the layout of a soccer field, these concepts are all around us. So, keep that in mind as you study—math is not just numbers and letters; it’s a tool for interpreting the world!

While you’re at it, don’t forget to explore additional resources like online practice tests and study groups to reinforce your understanding of the material. With the right tools in your toolbox, you’ll be more than ready to tackle the PERT head-on!