Question

the length of a rectangle is increased by 60% by what percent would the breadth be decreased to maintain the same area

Answer 1

let x = the decimal equiv decrease of the width
:
Write an area equation
Original area = new area
L * W = 1.6L * xW
Divide both sides by LW
1 = 1.6 * x
divide both sides by 1.6
 = x
x = .625, 
new width = .625*old width, therefore
1 - .625 = .375 * 100 = 37.5 decrease in the width to have the same area 

Answer 2

Length:
60% increase:
60% = 60/100 = 6/10 = 3/5
5(initial L)---------8(Final L)..... [60% of 5 = 3]
B1(initial B)------B2(Final B)
Given Area = constant = A
B1 = A/5
B2 = A/8
B1 : B2 = A/5 : A/8 = 1/5 : 1/8 = 8:5
8(Initial)-------5(Final B)
Change in breadth = 8-5 = 3
% change in breadth = 3/8 * 100 = 37.5%
Hence % decrease in breadth to make area constant = 37.5%