The perimeter of square A is 5 times greater than the perimeter of square B. How many times greater is the area of square A than the area of square B?

1 Answer
SagarStudy
Jan 31, 2016

If the length of each side of a square is #z# then its perimeter #P# is given by:

#P=4z#

Let the length of each side of square #A# be #x# and let #P# denote its perimeter. .
Let the length of each side of square #B# be #y# and let #P'# denote its perimeter.

#implies P=4x and P'=4y#

Given that: #P=5P'#

#implies 4x=5*4y#
#implies x=5y#
#implies y=x/5#

Hence, the length of each side of square #B# is #x/5#.

If the length of each side of a square is #z# then its perimeter #A# is given by:
#A=z^2#

Here the length of square #A# is #x#
and the length of square #B# is #x/5#

Let #A_1# denote the area of square #A# and #A_2# denote the area of square #B#.

#implies A_1=x^2 and A_2=(x/5)^2^ #

#implies A_1=x^2 and A_2=x^2/25 #

Divide #A_1# by #A_2#

#implies A_1/A_2=x^2/(x^2/25)#

#implies A_1/A_2=25#

#implies A_1=25A_2#

This shows that the area of square #A# is #25# times greater than the area of square #B#.

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