Solution:

20 units, 12 units & 15 units

As hard as it may sound, we have to just apply some basic algebraic equations to solve it.
Let the three sides be X, Y and Z. Now, the area of different surfaces is given:
X * Y = 240
Z * Z = 300
Y * Z = 180

Multiplying the obtained equations:
(X*Y) (X*Z) (Y*Z) = 240 * 300 * 180
X^2 * Y ^2 * Z^2 = 12960000
(X*Y*Z)^2 = 12960000
X*Y*Z = 3600

Now we know that X*Y = 240

Thus Z = 3600/240 = 15.

If we put the given values in the same manner, we get the three sides:
X = 20 units
Y = 12 units
Z = 15 units

Solution:

Pages 19, 20, 23, 37, 38, & 42 will also be missing

Solution:

Remove the same 2 matchsticks from each figure and move figure towards left 45 degrees, It forms the letters V W X Y.

Solution:

Blue could only be wearing white or red and we know that there is already someone else wearing the white shirt so Mr. Blue could only be wearing the red shirt.

Mr. White could have only been wearing a blue or a red shirt, and red is already taken, so Mr. White is wearing a blue shirt.

Mr. Red now has to be wearing a white shirt.

Solution:

60 minutes

Explanation:
Roy will be able to consume all the five tablets in an hour.

Tablet 1 will be taken in 0 min.
Tablet 2 will be taken in 15 min.
Tablet 3 will be taken in 30 min.
Tablet 4 will be taken in 45 min.
Tablet 5 will be taken in 60 min.

Solution:

The clerk said that every day the password is CHANGED. Changed is the password.

Solution:

He simply suggested that one of the brothers will be allowed to divide the land but he must take into consideration that it will be the other one who will have a choice of selecting his land between the two halves first.

Thus both will be happy in such manner.

Solution:

You better switch!

Your first choice has a 1/3 chance of having the car, and that does not change.<br>The other two doors HAD a combined chance of 2/3, but now a Goat has ben revealed behind one, all the 2/3 chance is with the other door.

Solution:

There can be two possibilities for the given situation.

One is if I run on the perimeter. Then, the lion will eventually catch me as the lion can follow my radius and then his trajectory will be half of the circle and not a spiral. Therefore, the lion will subsequently catch me in a finite amount of time.

Secondly if I don’t run on the perimeter, then clearly, I have an infinite amount of time before the lion catches me.

Solution:

I filled a glass full of water and held it over my head for 20 minutes.

Solution:

Put one red marble in one box and all other marbles in the 2nd box.

Probability :
50 + 24/49