Question

Question = One side of a rectangle is 3 cm shorter than the other side. If we increase the length of each side by 1 cm, then the area of the rectangle
will increase
by 18 cm^2. Find the lengths of all sides.

Answer 1

Let Length Of the Longer Side = x.
Shorter Side = x-3.
Area = x(x-3) cm².
Increase Length = (x + 1) & (x - 2) cm.
Area Of New Rect. = x(x-3) + 18  = (x+1)(x-2)
                               = x² - 3x + 18 = x(x-2) +1(x-2)
                               = x² - 3x + 18 = x² - 2x +x -2.
                               = x² - 3x + 18 = x² - x -2.
                               =               2x = 20
                               =                 x = 20/2 = 10.


x = 10.
So, Sides Of Rect. are 10 cm. & 7 cm Long.

Answer 2

let side of rectangle be x then other side will be x-3

then the area will be 
A=x*(x-3) 

now aac to question new side will be by adding 1
x+1 and x-3+1
⇒ x+1 and x-2

so new area will be A' for new sides
A'=(x+1)(x-2)

now acc to question
A'-A= 18
 (x+1)(x-2)-x(x-3)=18
$x^{2}$+x-2x-2-$x^{2}$+3x=18
x-2x+3x=18
2x=18
x=9 cm
so other side will be 6 cm