Question

A square has a side of $8cm$
The area of the square increase by $50\%$
Work out of percentage increase in the length of the side.

Answer 1

square of side 8 cm

Area of square increase 50%

percentage increase in length of side,

$\to$ Area of square = $l^2$

$\therefore =(8{)}^2$

$=64$

$\to$ Area increase 50%

So, $A^1=64+\frac{50}{100}\times 64$

$=64(1+\frac{1}{2})$

$=64\times \frac{3}{2}$

$\to$ new lengths $A^1=l^2$

$\therefore 64\times \frac{3}{2}=l^2$

$\therefore L^2=\frac{64\times 3}{2}$

$\therefore L=8.\sqrt{\frac{3}{2}}$

$\to$ percentage increase in length

$=\frac{L-l}{l}=\frac{8\sqrt{\frac{3}{2}-8}}{8}\times 100$

$=(\sqrt{\frac{3}{2}}-1)\times 100$

$=0.2247\times 100$

$=22.47\%$