Question

if the lenghth and breadth of a rectangle are doubled by what percentage is the area increased with solution​

Answer 1

Step-by-step explanation:

A1=lw

A2=(2w)(2l)

A2=4lw

A2=4A1

it is the 400% of the original are .Thus it increases by 300%

Answer 2

$\\ \\ \large\underline{ \underline{ \sf{ \red{given:} }}}$

• The lwngth and breadth of rectangle are doubled.

$\\ \\ \large\underline{ \underline{ \sf{ \red{to \: find:} }}}$

• Percentage increase in its area.

$\\ \\ \large\underline{ \underline{ \sf{ \red{solution:} }}}$

$\\ \bigstar \boxed{ \bf \:area \: of \: rectangle = l \times b }$

Initaially ,

• Length = l

• Breadth = b

Area(1) = lb

____________________

Finally ,

• Length = 2l

• Breadth = 2b

Area(2) = (2l)(2b)

Area(2) = 4lb

$\\ \boxed{\tiny\sf \: \% \: increase \: in \:a rea = \frac{final \: area - initial \: area}{initial \: area} \times 100} \\ \\ \\ \sf \: \% \: increase = \frac{4lb - lb}{lb} \times 100 \\ \\ \\ \sf \: \% \: increase = \frac{3{ \cancel{lb}}}{ \cancel{lb}} \times 100 \\ \\ \\ \sf \: \% \: increase = 300 \\ \\ \\ \sf \: \therefore \: \boxed{ \sf{ \blue{area \: is \: increased \: by \: 300\%.}}}$