Question

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

Answer 1

Let the length of the rectangle = x unit

And, width of the rectangle = y unit

Thus, Area of the rectangle = length * width = xy

Now, length of rectangle is increased by 60% .

So, New length of the rectangle = x + 60% of x = x + (60/100)*x = 8x/5

Let New width of the rectangle = y'

Thus, New Area = (8x/5) *y' = 8xy' /5

Since Area should be same, therefore,

Original Area = New Area

xy = 8xy'/ 5

y' = 5y/8

Thus,

Decrease in width = y - y' = y - 5y/8 = 3y/8

% Decrease = (Decrease in width) /(original value ) * 100 = (3y/8)/ y *100 = 37.5%

Hence, the width have to be decreased by 37.5% to maintain 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 %