05-05-2011, 03:39 PM
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
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