Aldo's company manufactures rectangular storage sheds. The sheds are made with aluminum side panels that measure 8 feet, 10 feet, 12 feet, and 15 feet along the bottom edge. For example, one possible shed measures 10 feet by 10 feet. Another possible shed measures 12 feet by 15 feet. List the measurements of all the possible sheds. How many different-sized sheds can be made?

Question

Aldo's company manufactures rectangular storage sheds. The sheds are made with aluminum side panels that measure 8 feet, 10 feet, 12 feet, and 15 feet along the bottom edge. For example, one possible shed measures 10 feet by 10 feet. Another possible shed measures 12 feet by 15 feet. List the measurements of all the possible sheds. How many different-sized sheds can be made?

Answer 1

You want to choose any 2 of the 4 measurements

which would be C(4,2) = 6
- easy to list

If the order of the dimensions matter, there would be 12 of them.
e.g. in a 10 by 12, you could have the door along the 10 ft side or the
12 ft side, they would be "different" sheds

You will have to decide how to interpret the question.

Answer 2

there are 4 side lengths that can be paired with any other length

so, 12 pairs (4 * 3) ... but, 8 by 10 is the same as 10 by 8
... 6 possible shed sizes

also, squares are rectangles ... an additional 4 sizes

Answer 3

c'mon, guys -- 4^2 = 16 shed sizes

his examples clearly indicate a size may be square

Answer 4

To find all the possible sheds that can be made, we need to consider the combinations of side panel lengths. The given side panels have lengths of 8 feet, 10 feet, 12 feet, and 15 feet. We can use these lengths to form the dimensions of the sheds.

One way to approach this is by finding all possible combinations of two different side panel lengths (since a shed has two adjacent sides). We can calculate the dimensions of the shed by pairing up each length with every other length.

Here are all the possible combinations:

1. Pairing 8 feet with 10 feet:
- Shed dimensions: 8 feet by 10 feet and 10 feet by 8 feet.

2. Pairing 8 feet with 12 feet:
- Shed dimensions: 8 feet by 12 feet and 12 feet by 8 feet.

3. Pairing 8 feet with 15 feet:
- Shed dimensions: 8 feet by 15 feet and 15 feet by 8 feet.

4. Pairing 10 feet with 12 feet:
- Shed dimensions: 10 feet by 12 feet and 12 feet by 10 feet.

5. Pairing 10 feet with 15 feet:
- Shed dimensions: 10 feet by 15 feet and 15 feet by 10 feet.

6. Pairing 12 feet with 15 feet:
- Shed dimensions: 12 feet by 15 feet and 15 feet by 12 feet.

To find out how many different-sized sheds can be made, we count the number of combinations. In this case, there are 6 combinations, so 6 different-sized sheds can be made.