Solution:

Original are of the rectangle = l*b where l= length and b = breadth
After the sides are increased by 100%, the area will increase by
= (((2l*2b)-(a*b))*100) / (a*b) = 300%

Solution:

Let x be the length of the room
Then according to the question, width will be x/2

As per the question
{(x*x/2)-(x-6) (x/2-6)}=108
9x =144
x=16

Thus the length of the room is 16.

Solution:

Decreases by 4%

Explanation:
New Length : 1.2
New Height : 0.8

Area = 1.2 * .8 = 0.96 (Decreases by 4%)

Solution:

60,000 Square Feet

Solution:

6ft

Explanation:
Given volume = 36, height = 4ft
Volume of Cylinder = Pi*square r*h
36 = Pi*squarer*4
Square r = 9
R = 3
Thus the radius of the cylinder = 3ft
Diameter = 2*radius = 6ft

Solution:

14.4 cms

Explanation:
Area of Square = Area of Rectangle
Side square = l*b
6 square = X(2.5)
36 = X(2.5)
X=14.4 cms.