Question

the lenth of a rectangle is increased by 60 by what percentage would the width have to decrease to maintain same area

Answer 1

he length of a rectangle is increased by 60% By what percent would the width have to be decreased to maintain the same area? 
:
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
 1/1.6 = 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

$\huge\mathfrak{Answer}$

Let the length 100 metre and breadth be 100m, then

New length = 160m, new breadth = x,

$\sf \: Then \: \: \: \: \: \: \: \: 160 \times x = 100 \times 100 \\ \\ \sf \implies \: x = \frac{100 \times 100}{160} \implies \: x = \frac{125}{2}$

$\therefore \: \rm \: decrease \: in \: breadth \: = 100 - \frac{125}{2} \% \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf \: 37 \: \frac{1}{2} \%$

So the answer is 37 and 1/2 %