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. Show work.

Answer 1

Solutions 

Let x be the length of the longer side x>3, then the other side's length is x−3. Then the area is S1 = x(x - 3) cm2. After we increase the lengths of the sides they will become (x+1) and (x−3+1)=(x−2) cm long. Hence the area of the new rectangle will be 

A1+18=A2

x(x−3)+18=(x+1)(x−2)

x²−3x+18=x²+x−2x−2

2x=202

x=10

So, the sides of the rectangle are 10 cm and (10−3)=7 cm long.

Answer 2

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.