Question

The ratio of the heights of two similar rectangular prisms is 2:3. What is the ratio of their lateral areas?

Answer 1

The area of two similar rectangles is equal to the square of their ratio.
Example: Rectangle A = 2x4, Rectangle B = 3x6. A's Area: 8, B's Area = 18. \[\frac{ 8 }{ 18 } = \frac{ 4 }{ 9 } = \left( \frac{ 2 }{ 3 } \right)^2\]

Answer 2

So what is the ratio of the lateral lines of two similar rectangular prisms with the ratio as 2:3?

Answer 3

8:27

2:5

4:9

1:0.33

Answer 4

The lateral lines of both of the similar rectangles will have a ratio of 4:9, which equals 2:3.
For example: Rectangle A = 1x5, Rectangle B = 2x10, Rectangle C = 3x15.
Also, the definition of similar rectangles states that two similar rectangles will have the same ratio for both their height and width.

Answer 5

Oh okay so the answer is 4:9?

Answer 6

Yes, sorry for answering the wrong question at first.

Answer 7

It's okay, I'm not good with math. All the numbers confuse me, wanna help me with another one? lol

Answer 8

lol, sure, why not?

Answer 9

Haha, okay as long as you explain how to do it I should be able to get it. I'm not asking you to do it for me :)
Part 1: Create and provide the dimensions for two similar figures of your choosing.
Part 2: What is the similarity ratio of these figures along with the ratio of their surface area and volume?
Part 3: Show your work, either using the actual volumes or using the formula, that the volume ratio is true.

Answer 10

Well, personally, I'd choose two small cubes and run the numbers on them, since that would make the math easier.

Answer 11

So what do I need to do? haha o.O

Answer 12

For the first part, give two pairs of three dimensions (one for each cube) that define the shape (such as 1x1x1). Since all cubes are similar, that part takes care of itself.

Answer 13

You with me so far?