Scale problem

[azorman]

This math problem was given to my kid and I just can't figure how the teacher is reaching her answer. Here is the problem:

The scale of the area of the door in the toy to the area of the physical door is 1/2500. The original toy has a rectangle door with the height being 240cm. What is the height of the door in the model? The answer she's giving is 4,8cm but my modest math knowledge tells me this problem does not have an answer, or better said, can have multiple answers.

Thanks very much for your help.

P.S.
I apologize but I made a mistake when I posted the questions initially; it is corrected now.

 

[mmm4444bot]

This math problem was given to my kid and I just can't figure how the teacher is reaching her answer. Here is the problem:

A toy is built at at a scale of 1/2500.

The original toy has a rectangle door with the height being 240cm.

What is the height of the door in the model?

The answer she's giving is 4,8cm but my modest math knowledge tells me this problem does not have an answer, or better said, can have multiple answers.

Thanks very much for your help.

When a scaled-down model of something is made at a specific scale, then there is one and only one scaled-down model possible (not infinite scaled-down models).

The scale 1/2500 means that 1 centimeter in the model equals 25 meters in the original (25 m = 2500 cm).

That is, 2500 cm gets reduced to 1 cm, when using the scale 1:2500



There are two toys. The original toy's door measurement is 240 cm, and they made a new toy that is 1/2500th as big as the original.

Multiply original measurements (in cm) by 1/2500, to convert into scaled measurements (also in cm).



One could also set-up a proportion, for this exercise.

1/2500 = ?/240



I'm not sure what the student's class has been doing. Now sure where 4,8 cm came from, either. The door in the scaled model will be tiny (close to 1 mm).

Cheers :cool:

 

[azorman]

When a scaled-down model of something is made at a specific scale, then there is one and only one scaled-down model possible (not infinite scaled-down models).

The scale 1/2500 means that 1 centimeter in the model equals 25 meters in the original (25 m = 2500 cm).

That is, 2500 cm gets reduced to 1 cm, when using the scale 1:2500



There are two toys. The original toy's door measurement is 240 cm, and they made a new toy that is 1/2500th as big as the original.

Multiply original measurements (in cm) by 1/2500, to convert into scaled measurements (also in cm).



One could also set-up a proportion, for this exercise.

1/2500 = ?/240



I'm not sure what the student's class has been doing. Now sure where 4,8 cm came from, either. Cheers :cool:

Thanks very much... you made me see I had made a mistake on my original post.

 

[JeffM]

This math problem was given to my kid and I just can't figure how the teacher is reaching her answer. Here is the problem:

A toy is built at at a scale of 1/2500. The original toy has a rectangle door with the height being 240cm. What is the height of the door in the model? The answer she's giving is 4,8cm but my modest math knowledge tells me this problem does not have an answer, or better said, can have multiple answers.

Thanks very much for your help.

The problem undoubtedly has a unique answer. But I do not think that the problem is being given accurately. A door with a height of 240 centimeters has a height of 2.4 meters, which is larger than the doorway of an average house. In other words, the original toy seems to be bigger than a house. No wonder they need to scale it down.

Here is what I suggest. Have your son visit our introductory site at http://www.freemathhelp.com/forum/threads/78006-Read-Before-Posting

Then add a posting to this thread giving the information requested and the exact words of the problem.

 

[HallsofIvy]

If the toy is 1/2500 of the original, multiply any length on the original by 1/2500 to get the corresponding length on the toy. In particular, if the original has a door with height 240 cm then the corresponding door on the toy will have length \(\displaystyle \frac{240}{2500}= 0.96\) cm. That is not the "4.8 cm" you quote but I can't imagine why you think there could be many answers.

 

[azorman]

The problem undoubtedly has a unique answer. But I do not think that the problem is being given accurately. A door with a height of 240 centimeters has a height of 2.4 meters, which is larger than the doorway of an average house. In other words, the original toy seems to be bigger than a house. No wonder they need to scale it down.

Here is what I suggest. Have your son visit our introductory site at http://www.freemathhelp.com/forum/threads/78006-Read-Before-Posting

Then add a posting to this thread giving the information requested and the exact words of the problem.

You're absolutely right, my mistake, I corrected the post. Thanks very much.

 

[azorman]

If the toy is 1/2500 of the original, multiply any length on the original by 1/2500 to get the corresponding length on the toy. In particular, if the original has a door with height 240 cm then the corresponding door on the toy will have length \(\displaystyle \frac{240}{2500}= 0.96\) cm. That is not the "4.8 cm" you quote but I can't imagine why you think there could be many answers.

Absolutely right, I made a mistake when I posted; I already corrected it. Thanks very much.

 

[mmm4444bot]

\(\displaystyle \frac{240}{2500}= 0.96\) cm

That should be 0.096 cm

 

[JeffM]

Absolutely right, I made a mistake when I posted; I already corrected it. Thanks very much.

AHA

The scaling is being done in terms of area, not length.

That is, an area of 2500 square centimeters is being scaled down to an area of 1 square centimeter.

But area of a square is the square of the length of a side. So a square with an area of 2500 square centimeters has a side with a length of

\(\displaystyle \sqrt{2500} = \sqrt{25 * 100} = \sqrt{25} * \sqrt{100} = 5 * 10 = 50.\)

And a square with an area of 1 square centimeter has a side with length of 1 centimeter.

So the linear scaling factor is that every 50 centimeters is reduced to 1 centimeter.

And \(\displaystyle \dfrac{240}{50 } = 4.8.\)

Can you explain it to your son now?

PS It is probably better to have your son come here directly to ask. That way, there are fewer problems in translation. Please make sure he first reads

http://www.freemathhelp.com/forum/threads/78006-Read-Before-Posting

 

[azorman]

AHA

The scaling is being done in terms of area, not length.

That is, an area of 2500 square centimeters is being scaled down to an area of 1 square centimeter.

But area of a square is the square of the length of a side. So a square with an area of 2500 square centimeters has a side with a length of

\(\displaystyle \sqrt{2500} = \sqrt{25 * 100} = \sqrt{25} * \sqrt{100} = 5 * 10 = 50.\)

And a square with an area of 1 square centimeter has a side with length of 1 centimeter.

So the linear scaling factor is that every 50 centimeters is reduced to 1 centimeter.

And \(\displaystyle \dfrac{240}{50 } = 4.8.\)

Can you explain it to your son now?

PS It is probably better to have your son come here directly to ask. That way, there are fewer problems in translation. Please make sure he first reads

http://www.freemathhelp.com/forum/threads/78006-Read-Before-Posting

Got it! Thanks very much! I thought I had... you do know that the 240 is not the area of the door, right? 240 is the length.

 

[JeffM]

you do know that the 240 is not the area of the door, right? 240 is the length.

Exactly, that is why we had to find the scaling factor for length rather than use the scaling factor for area.

 

[HallsofIvy]

Oh, dear! The problem is not with my math but I just can't read! I completely missed the mention of "area".

If the area is scaled by 1/2500, and area is "length times length" or "lengths squared", lengths are scaled by \(\displaystyle \frac{1}{\sqrt{2500}}= \frac{1}{50}\). A length of 240 cm would be scaled to \(\displaystyle \frac{240}{50}= 4.8 cm.\)

 

[JeffM]

Oh, dear! The problem is not with my math but I just can't read! I completely missed the mention of "area".

If the area is scaled by 1/2500, and area is "length times length" or "lengths squared", lengths are scaled by \(\displaystyle \frac{1}{\sqrt{2500}}= \frac{1}{50}\). A length of 240 cm would be scaled to \(\displaystyle \frac{240}{50}= 4.8 cm.\)

It was not in the original post. It was added by edit. Very confusing.

 

[HallsofIvy]

And I confuse very easily! But at least I know my mind is not going- not yet, anyway.

 

[azorman]

And I confuse very easily! But at least I know my mind is not going- not yet, anyway.

Thank you everyone and I apologize again for the confusion; just wanted to make sure you all know I appreciate your help. Congratulations on keeping up this site.