Question

if the side of a square be increased by 50% find the percent increase in area
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Answer 1

Let the side of the square be x

Area of thesquare =x^2

50% of the side=x/2

New side=x+x/2=3x/2

Area of the square with a new side=3x/2^2=9x^2/4

Increased %=increased area/actual area×100

increased area=(9x^2/4)-x^2=5x^2/4

increased %={(5x^2/4)/x^2}×100=125%

Answer 2

$\huge\bold\red{Question}$

If the side of a square be increased by 50% find the percent increase in area

$\huge\bold\green{Solution}$

Let side of square = $\bold{x}$

Old Area =$\bold{x^2}$

After 50% increase in side

side length= $\bold{x+50\%\:of\:x}$

= $\bold{ \frac{3}{2}x}$

Area Increase= $\bold{(\frac{3}{2} x)^{2}}$

= $\bold{ \frac{9}{4} {x}^{2}}$

Percentage increase in are

$\bold{\frac{Area\: Increase-Old \:Area }{Old\:Area} \times 100}$

$\bold{ \frac{\frac{9}{4}{x}^{2} - {x}^{2} }{ {x}^{2} } \times 100}$

$\bold{\frac{5 {x}^{2} }{ {4x}^{2} } \times 100}$

$\bold{= 12.5\%}$