Question

The length of a rectangle is increased buy 10 % while its breadth is decreased by 10%. What is the consequent percentage change in the area of the rectangle?

Answer 1

Suppose the length of rectangle to be 100 units and width to be 10 units.
Length (10% increase)=$100+\frac{10}{100}\times 100$= 100 + 10= 110 units
Width (10% increase)= 10+$\frac{10}{100}\times 10$= 10+1= 11 units
Area of rectangle= $l\times b$
$=100\times 10=1000uni{t}^2$
Area of rectangle(10% increase in l and b) = l*b
$=110\times 11$
$=1210uni{t}^2$
Change in area= 1210–1000= 210 unit^2
%age increase in its area= $\frac{\text{Change in area}}{\text{Actual area}}\times 100$
=$\frac{210}{1000}\times 100$
=$21\%$