Question

Lengt of a rctangle is increased by 20%.Breadth is increased by 30%.What is the overall change in the area

Answer 1

Let the length of original rectangle be l and breadth be b.

$\boxed{Area A= l \times b}$

$\bold{ACCORDING \: TO \: QUESTION }$

Length is increased by 20%.

So, new length will be,

$\mathsf{l_2 = l +20 \% l}$

$\mathsf{l_2= l - \frac{20}{100} \times l}$

$\mathsf{l_2= l + \frac{1}{5} \times l}$

$\mathsf{l_2= \frac{5 l + 1l }{5} }$

$\mathsf{l_2 = \frac{6 l }{5}}$

Breadth is increased by 30 %

So, new breadth will be,

$\mathsf{b_2 = b+ 30 \% l}$

$\mathsf{b_2= b + \frac{30}{100} \times l}$

$\mathsf{b_2= b + \frac{3}{10} \times l}$

$\mathsf{b_2= \frac{10 b + 3b }{10}}$

$\mathsf{b_2 = \frac{13b}{10}}$

New area will be,

${AREA = \frac{6 l }{5} \times\frac{13b}{10} }$

$\boxed{A_2= \frac{39lb}{25}}$

So, the new area will be, $\frac{39lb}{25}$ .



Overall change = $A_2 - A$

Overall change = $\frac{39lb}{25} - lb$

Overall change = $\frac{14}{25}lb$

So, new area will be increased by$\frac{14}{25}$