Question

The length of a rectangular field is increased by 50% and its breadth is decreased by 50% to form a new rectangular field. Find the % change in the area of the field.

Answer 1

Let the length of rectangle be a

And width of rectangle be b

Area $=ab$

Now,

New length $=a+50$% of $a$

$=a+\frac{50a}{100}$

$=a+\frac{a}{2}$

$=\frac{3a}{2}$

New width $=b-50\%$ of $b$

$=b-\frac{b}{2}$

$=\frac{b}{2}$

New Area $=\frac{3a}{2}\times \frac{b}{2}$

$=\frac{3ab}{4}$

Decrease in Area $=ab-\frac{3ab}{4}$

$=\frac{ab}{4}$

% of Decrease in Area $=[\frac{ab}{4}\times 100]/ab$

= $\frac{100}{4}$

= $25$ %