Geometry, and a logic question

[Brandenx781]

Can someone please help me on this little brain teaser? I just need an answer, and an explanation on how you got the answer.

Please and thanks!

Geometry
1. A square and four congruent rectangles are arranged in a larger square. The smaller square and each of the rectangles have the same perimeter. Determine the ratio of the length of a side of the larger square to the length of a side of the smaller square.

http://imageshack.us/photo/my-images/848/unledbqc.jpg/

2. A container in the shape of a rectangular solid with dimensions 4 x 5 x 10 is placed so that its height is 10. Water fills the container to a height of 6. The container is then turned so that the base dimensions are 4 x 10. Determine the height of the water in the container.

Logic
3. If it takes 12 minutes to cut a log into 4 pieces, how many minutes will it take to cut a log into 3 pieces?

[BlackChaos]

1. Consider the perimeter of a rectangle, which is equal to 2(l+b)
Since the perimeter of the rectangle is equal to perimeter of smallar square, perimeter of smaller square is also equal to 2(l+b)

Now, perimeter of a sqare is 4x(side of square).
Therfore, length of square is equal to perimeter divided by 4, i.e. (l+b)/2

Now, according to the figure, the side of the larger square consists of one length and one breadth of a rectangle.
Therefore, side of larger square is (l+b)

So, ratio between the side of larger square and smaller square is,
(l+b):(l+b)/2
= 1:2

Answer is 1:2

2. Dimensions of the cuboid in the first position= 4x5x10
Dimensions of the cuboid in the second position= 4x10x5

Since we need to find height of water level, lets substitute it in both the given steps.

So, taking the height as equal to height of water level,
Dimensions of the cuboid in the first position= 4x5x6
Dimensions of the cuboid in the second position= 4x10xß

ß is the height of water we need to find.

Volume of a cuboid is lxbxh.
Now, since volume is constant, we can equate the two equations like so:

4 x 5 x 6 = 4 x 10 x ß
120 = 40ß
Therfore, ß = 3 units

Answer is 3 units

3. This is simple logic.
If cutting 4 logs takes 12 minutes, how much time does it take to cut 1 log?

So, time taken to cut one log is = 12/4 = 3 minutes

Therfore, time taken to cut three logs = 3 x 3 = 9 minutes.

Answer is 9 minutes

[Brandenx781]

1. Consider the perimeter of a rectangle, which is equal to 2(l+b)
Since the perimeter of the rectangle is equal to perimeter of smallar square, perimeter of smaller square is also equal to 2(l+b)

Now, perimeter of a sqare is 4x(side of square).
Therfore, length of square is equal to perimeter divided by 4, i.e. (l+b)/2

Now, according to the figure, the side of the larger square consists of one length and one breadth of a rectangle.
Therefore, side of larger square is (l+b)

So, ratio between the side of larger square and smaller square is,
(l+b)l+b)/2
= 1:2

Answer is 1:2

2. Dimensions of the cuboid in the first position= 4x5x10
Dimensions of the cuboid in the second position= 4x10x5

Since we need to find height of water level, lets substitute it in both the given steps.

So, taking the height as equal to height of water level,
Dimensions of the cuboid in the first position= 4x5x6
Dimensions of the cuboid in the second position= 4x10xß

ß is the height of water we need to find.

Volume of a cuboid is lxbxh.
Now, since volume is constant, we can equate the two equations like so:

4 x 5 x 6 = 4 x 10 x ß
120 = 40ß
Therfore, ß = 3 units

Answer is 3 units

3. This is simple logic.
If cutting 4 logs takes 12 minutes, how much time does it take to cut 1 log?

So, time taken to cut one log is = 12/4 = 3 minutes

Therfore, time taken to cut three logs = 3 x 3 = 9 minutes.

Answer is 9 minutes

OH MY GOD! THANK YOU SO MUCH! <3

[BlackChaos]

You're welcome
Was this your homework or something? lol

[Brandenx781]

You're welcome
Was this your homework or something? lol

It was actually some extra credit questions that adds 5 point for each questions right to a quiz grade. I had 5 problems.

[BlackChaos]

Alright then. I hope they were correct