Question

If the side of a square is increased by 50% find the percentage increase in its area

Answer 1

 a variable X changes by A% and another variable Y changes by B%, then overall net change when the two variables are multiplied is given by :

A + B + AB/100

If the change is “increase” it is positive & if the change is “decrease” it is negative.

so for increasing 50% in side so

according to above concept


What will be increase in area of a circle if radius is increased by 50% ?

Ans : 50 + 50 + (50 x 50)/100 = 125%

Answer 2

$\underline \bold{Solution:-}$

Let the side of square be x unit.

Area of square
$= {side}^{2} \\ \\ = {x}^{2} \: unit$

When the side is increased by 50%.

New side = earlier side + 50% of earlier side

$= x + \frac{50}{100} \times x \\ \\ = x + \frac{x}{2} \\ \\ = \frac{2x + x}{2} \\ \\ = \frac{3x}{2}$

New Area

$= {(\frac{3x}{2})}^{2} \\ \\ = \frac{9{x}^{2}}{4}\: unit$

Area increase = New Area - Old Area

$= \frac{9{x}^{2}}{4} - \frac{3x}{2}\\ \\ = \frac{3x}{4}$

Percentage increase in Area

$= \frac{Area \: increase}{old \: Area} \times 100 \\ \\ = \frac{\frac{3x}{4}}{4x} \times 100 \\ \\ =\frac{3}{4x} \times 25 \\ \\ = 18.74\%$