will the area of a rectangle change if you increase the length by 20% and decrease the width by 20%? If so, by what percentage?

Question

 word problem

Answer 1

Let x = length of the original rectangle and y = width of the original rectangle

 

So, Area = A = xy

 

If the length is increased by 20% and the width is decreased by 20%, the area of the new rectangle is (x + 0.20x)(y - 0.20y) = (1.2x)(0.8y)

 

                                                                            = 0.96xy

 

                                                                             = 0.96A

 

So, the area of the new rectangle is 96% of the original area.  In other words, the area decreased by 4%.