How to Calculate the Area of Your New Office Space: A Practical Guide

A woman is looking for a bigger square office. She finds an office twice the area of her current office. If the perimeter of her current office is 88 feet, how many square feet is the new office?

• A. 176 sq ft
• B. 196 sq ft
• C. 144 sq ft
• D. 128 sq ft

Answer: (A)

The new office is twice the area of the woman's current office. This means that the new office is double the size of the current office. Since the current office is a square, this also means that the new office has twice the length and width of the current office. Double the length and width of a square will result in a square that is twice as large in area. Therefore, the new office has an area of 176 sq ft. The other options are incorrect because they do not reflect the information given in the question. Option B (196 sq ft) is not double the size of the current office and has a perimeter of 98 feet, which does not match the given perimeter of 88 feet. Option C (144 sq ft) has a perimeter of 60 feet, which is not double the perimeter of the current office. Option D (128 sq ft) is not double the size of the current office and has a perimeter of 64 feet, which also does not match the given perimeter of 88 feet. Therefore, the best answer is A (176 sq ft) as it is the only option that meets the criteria given in the question.

When you're looking for a new office space, there's a lot more than just the aesthetics involved—you need to get your numbers right. Let's break this down so it makes crystal clear sense, especially if you're preparing for that ASVAB test!

You know what? Office size matters more than you might realize. It impacts everything, from workplace morale to how efficiently space is used. So, when our friend is on the hunt for a bigger square office, she stumbles upon an opportunity to double the area of her current space. Sounds exciting, right? But, how do we figure out the specifics here?

Unpacking the Problem

First things first, let’s talk about her current office. The perimeter is given as 88 feet. Remember your geometry from school? The formula for the perimeter of a square is simply (P = 4 \times s) where (s) is the length of one side.

Here’s the thing:

[ 4 \times s = 88 \text{ feet} ]

Now, solving for (s) (the length of one side), we divide both sides by 4:

[ s = \frac{88}{4} = 22 \text{ feet} ]

Awesome, right? Now we know that each side of her current office is 22 feet long. Next, let’s find out the area of her current office. The area (A) of a square is calculated with (A = s^2).

So, plugging in the value we calculated:

[ A = 22^2 = 484 \text{ square feet} ]

Now, here’s where it gets exciting. Our lady wants to find a new office that’s twice this size. So, we’ll multiply the area of the current office by 2:

[ 2A = 2 \times 484 = 968 \text{ square feet} ]

But wait! Didn’t we promise to figure out the dimensions for the new office? Hang tight, because here’s where we break it down further.

Understanding the New Office’s Size

The new office, being double the area of the current one, needs some number-crunching. If the area of the new office is 968 square feet, it’s important to remember, to work it out in square dimensions, we look for a square that has the same area.

So we’re trying to find the new side length (s_{new}):

[ s_{new}^2 = 968 ]

To find out (s_{new}):

[ s_{new} = \sqrt{968} \approx 31.1 \text{ feet} ]

Now take a second to check our perimeter for this size. The perimeter of the new office would be:

[ P = 4 \times s_{new} = 4 \times 31.1 \approx 124.4 \text{ feet} ]

In essence, this journey through numbers shows just how important it is to understand area and perimeter when planning an office space.

Answer to the Office Dilemma

But let’s get back to the choices presented in the original problem statement regarding square footage. The choices were 176 sq ft, 196 sq ft, 144 sq ft, and 128 sq ft.

With our friend’s current office being 484 sq ft, and her desire for a new office that is twice that area, it turns out the answer to the correct area is not explicitly mentioned in your options! It seems something went off the rails. The calculated area for the new office should be a whopping 968 sq ft.

And here’s a shoutout for the sizes of those options:

• 176 sq ft—isn't even double the current space square footage.

• 196 sq ft—also falls short.

• 144 sq ft—the numbers don’t even add up for a new office at that size!

• 128 sq ft—is definitely not a contender.

So let’s bring it all back home. For office space planning—whether for a cozy home office or a bustling work location—understanding the basics of area and perimeter can literally open doors to new opportunities. Next time you’re upgrading, remember: the numbers do matter, and getting it right is worth the effort!