How many square rug of 17cm by 17cm is needed for a square room of size 4.2m?

[chijioke]

Estimate the number of square rug of size 17cm by 17cm that is needed for a square room of size 4.2m.
This is my work:
[math]Area~ of ~square~ rug~= 17cm ×17cm=289~cm^2[/math][math]\text{Area of floor of square room}=420cm×420cn=176400cm^2[/math]Number of square rug required to completely cover the room is
[math]\frac{176400}{289}=610[/math]Is my work and solution correct?

 

[khansaheb]

Estimate the number of square rug of size 17cm by 17cm that is needed for a square room of size 4.2m.
This is my work:
[math]Area~ of ~square~ rug~= 17cm ×17cm=289~cm^2[/math][math]\text{Area of floor of square room}=420cm×420cn=176400cm^2[/math]Number of square rug required to completely cover the room is
[math]\frac{176400}{289}=610[/math]Is my work and solution correct?

How are you going to lay those rugs?

Are you allowed to cut those rugs?

Are you allowed to overlap ?

 

[Dr.Peterson]

Estimate the number of square rug of size 17cm by 17cm that is needed for a square room of size 4.2m.
This is my work:
[math]Area~ of ~square~ rug~= 17cm ×17cm=289~cm^2[/math][math]\text{Area of floor of square room}=420cm×420cn=176400cm^2[/math]Number of square rug required to completely cover the room is
[math]\frac{176400}{289}=610[/math]Is my work and solution correct?

It's a good estimate, based on area.

To make a more accurate "estimate", you could think about how the rugs would actually fit in the room. How many can fit along each side of the room? If the entire floor doesn't have to be covered, what is the largest number of whole rugs you could fit? If the floor does have to be covered, how could you do it by cutting rugs?

But you don't have to do all this; what you did is probably what is expected. Doing more is a way to grow in your understanding of this sort of practical problem. Will your estimate have been high or low?

 

[stapel]

Estimate the number of square rug of size 17cm by 17cm that is needed for a square room of size 4.2m.

Just a guess, but did the exercise really say "4.2m" (which is a length, in which case we need the other dimension) or maybe did it say "4.2m²" (which is an area)?

This is my work:
[math]Area~ of ~square~ rug~= 17cm ×17cm=289~cm^2[/math][math]\text{Area of floor of square room}=420cm×420cn=176400cm^2[/math]Number of square rug required to completely cover the room is
[math]\frac{176400}{289}=610[/math]Is my work and solution correct?

Assuming that they're wanting a mathematical answer, rather than a real-world answer, your method is correct. However, if you round *down* (as you did), then there must necessarily be some portion of the floor which is not covered. So you're probably supposed to round *up* for your answer (which would still not be the correct "real world" answer).

Eliz.

 

[NotJeffM]

Excellent answers from other helpers, but what this reenforces for me is how important it is to give the actual words of the problem exactly and completely every time. Your answer may be sensible if “size” is a typo for “side,” but even then it is not clear whether yours is the best answer as the responses from the other helpers show.

 

[chijioke]

Just a guess, but did the exercise really say "4.2m" (which is a length, in which case we need the other dimension) or maybe did it say "4.2m²" (which is an area)?

It might interest you that there are some options for the solutions. But it seems none of the options matches my answer.

 

[stapel]

It might interest you that there are some options for the solutions. But it seems none of the options matches my answer.View attachment 35703

Huh. The "4.2m" is in the original exercise, so clearly the exercise is the problem, not you.

You might want to point this out to your instructor.

Eliz.

 

[Dr.Peterson]

It might interest you that there are some options for the solutions. But it seems none of the options matches my answer.View attachment 35703

You are supposed to show us the entire problem, not just part of it, in order to avoid wasting our time. The more information we have; the more easily we can be sure of the problem.

Please show us all of it now, so we can check the rest. So far, I don't see an interpretation that works.

 

[chijioke]

You are supposed to show us the entire problem, not just part of it, in order to avoid wasting our time. The more information we have; the more easily we can be sure of the problem.

Please show us all of it now, so we can check the rest. So far, I don't see an interpretation that works.

Can you see the entire problem now?

 

[Dr.Peterson]

View attachment 35713View attachment 35714
Can you see the entire problem now?

Yes; unfortunately, there is no information you had not given to us.

Correcting the grammar of the problem, it is this:

Estimate the number of square rugs of size 17 cm by 17 cm that are needed for a square room of size 4.2 m by 4.2 m.​

A. 400 B. 420 C. 441 D. 514 E. 840​

(I'm trusting that 4.2 m means what it says, and not 4.2 m^2.)

But as you found, none of the choices fits any interpretation of the situation I have thought of. On the other hand, "estimate" means that you don't have to have an exact number, so you could choose whichever number is closest to your estimate.

But that doesn't give me a good impression of the creator of the problem. In particular, it is not at all clear what "needed" means.

If it means we want to cover as much of the floor as possible with whole rugs, then we can fit 420/17 = 24.7 rugs along a side, but we have to round down to 24, and the answer is 24^2 = 576.

If it means to cover the entire floor with pieces of rug cut in any way necessary, then we need an area of 420^2 = 176,400 cm^2, with each rug being 17^2 = 289 cm^2, so we can fit 176,400/289 = 610.38, and we have to round up to 611.

If we needed to cover the entire floor area, cutting each rug no more than once, then we could fill the empty space around the 576 rugs with pieces of another 24+24+1 rugs, for a total of 576+24+24+1 = 625 rugs. (That is, we round up to 25 rugs on a side and cut off the extra.)

Clearly the room can't be 4.2 m^2, as that would have sides 2.05 m = 205 cm, and we could fit only 12 rugs on a side, for a total of about 144 rugs.

But none of these answers is anywhere near the choices. I was hoping there might be something in the problem statement or its context that would define how the rugs are to be placed, or that a number might have been copied incorrectly.

I think it is simply a bad problem.