Question

किसी आयत की लंबाई में 10% की वृद्धि तथा चौड़ाई में 10% की कमी की जाए तो उसके क्षेत्रफल प्रतिशत प्रभाव कितना होगा

Answer 1

1% reduction in area

Answer 2

Answer:

The area of rectangle reduced by 1%.

Step-by-step explanation:

Let the length of rectangle be l and the width of the rectangle be w.

The area of a rectangle is

$A=length\times width$

$A=l\times w$

Length increased by 10%. New length is

$l=l+\frac{10}{100}l=l+0.1l=1.1l$

Width decreased by 10%. New width is

$w=w-\frac{10}{100}w=w-0.1w=0.9w$

The new area is

$A_1=1.1l\times 0.9w=0.99lw$

% change in area is

$\frac{A_1-A_0}{A_0}\times 100=\frac{0.99lw-lw}{lw}=\frac{-0.01lw}{lw}\times 100=-1%$

Therefore the area of rectangle reduced by 1%.