Question

the side of a rectangle are 20 cm And 15 CM if each side is increased by 20% find the percentage increase in the area​

Answer 1

Answer:

$\sf{The \ increase \ in \ area \ is \ 44\%.}$

Given:

$\sf{The \ side \ of \ a \ rectangle \ are \ 20 \ cm}$

$\sf{and \ 15 \ cm}$

To find:

$\sf{If \ each \ side \ is \ increased \ by \ 20\%} \\ \sf{find \ the \ percentage \ increase \ in \ the \ area.}$

Solution:

$\sf{For \ original \ rectangle,} \\ \\ \sf{\leadsto{Length=20 \ cm \ and \ Breadth=15 \ cm}} \\ \\ \boxed{\sf{Area \ of \ rectangle = Length\times \ Breadth}} \\ \\ \sf{\therefore{Area=20\times15}} \\ \\ \sf{Area=300 \ cm^{2}}} \\ \\ \sf{The \ area \ of \ original \ rectangle \ is \ 300 \ cm^{2}} \\ \\ \sf{20\% \ of \ 20=\dfrac{20}{100}\times20} \\ \\ \sf{20\% \ of \ 20=4 \ cm} \\ \\ \sf{\therefore{Length \ after \ increasing \ by \ 20\% = 20+4 =24 \ cm}} \\ \\ \sf{20\% \ of \ 15=\dfrac{20}{100}\times15} \\ \\ \sf{20\% \ of \ 15 = 3 \ cm} \\ \\ \sf{\therefore{Breadth \ after \ increasing \ by \ 20\%=15+3=18 \ cm}} \\ \\ \sf{Area \ of \ rectangle \ with \ increased \ sides=24\times18} \\ \\ \sf{\therefore{Area \ of \ rectangle \ with \ increased \ sides=432 \ cm^{2}}} \\ \\ \sf{Difference \ in \ area=432-300=132 \ cm^{2}} \\ \\ \sf{Let \ the \ increase \ in \ be \ x\%} \\ \\ \sf{\therefore{132=\dfrac{x}{100}\times300}} \\ \\ \sf{\therefore{x=\dfrac{132}{3}}} \\ \\ \sf{\therefore{x=44\%}} \\ \\ \purple{\tt{\therefore{The \ increase \ in \ area \ is \ 44\%.}}}$