What is the mathematical way to do question such as:?

Question

Tyler is drawing a picture of the cruise ship that he sailed on last summer. What would be the best scale to use if he is drawing the picture on a piece of notebook paper 8 in. by 11 in. and the cruise ship was 1,600 feet long?
OR

Lisa is drawing a picture of the cruise ship that she sailed on last summer. What would be the best scale to use if she is drawing the picture on a piece of notebook paper 8 in. by 11 in. and the cruise ship was 1800 feet long?

And this is NOT homework; they were just questions I found on the internet for practice

Answer 1

This is called drawing to scale.

For ships, an architectural scale is typically used.

For example, a scale of 1/2 inch=100 feet may be used. This would mean that 1 inch would represent 200 actual feet, that 2 inches would represent 400 actual feet, and so on.

The 1,600 foot and 1800 foot ship lengths would fit along the 11 inch direction of the paper because the scale would:
1 - mean that 8 inches on the paper would represent 1,600 actual feet, and
2 - mean that 9 inches on the paper would represent 1,800 actual feet.

The beam, or width of each ship is not given, but the general proportion of ships suggests that their widths would probably fit along the 8 inch width of the paper.

As far as the heights of the ships fitting, since the their heights are not given, I cannot figure out if those would fit the width. But, the principle that some scale be used would still apply.

I hope this helps.

Answer 2

Assume that the drawing will be in the landscape mode: that is, the 11 inch side will be used to include the ship's length and the 8.5 inch side would be used to show the ship's height.

Assume a border of .5 inch all the way around. This would leave a drawing area of 10 by 7.5 inches.

So in Tyler's case 10 inches must represent 1600 feet. So the scale should be 1 inch 160 feet.

In Lisa's case 1 inch = 180 feet.

Answer 3

The scale the the ratio of the size of the drawing divided by the size of the ship. 1/8 scale means that one inch on the drawing represents 8 inches on the real thing. Or the drawing is 1/8 the size of the real thing.

So the paper is 11 inches long. The ship is 1600*12 = 19,200 in. The scale would be 11 / 19,200 if you want the ship to be exactly the length of the paper. If you want a half-inch margin, the scale would be 10 / 19,200, which simplifies to 1 / 1,920.

Answer 4

So you would want 1600 ft to equal about 10 inches (leaving a little room on the sides and using the paper in landscape orientation).

That is the same as 1 inch = 160 ft.

For the other:

1 inch = 180 ft.

Bozo

Answer 5

the 2nd part with lisa