Ratio Of Area of Rectangle To Area Of Square Is 1:4, Ratio Of Perimeter Of Rectangle To Perimeter Of Square Is 1:2. If The Length Is 5 cm Then Find The Area Of Square

One side of Rectangle =5, given

Other side of Rectangle = x

Side of Square =y

Area of Rectangle =5*x

Area of Square = y2

5x:y2 =1:4

y2 =20x

Now,

Perimeter Of Rectangle= 2 (5+x)

Perimeter Of Square = 4y

2 (5+x) : 4y=1:2 ,

5+x=y

Squaring both side

25+x2 +10x =y2

25+x2 +10x =20x

x2 -10x+25=0

x=5

y2=20x =20*5 =100

Area = y2 =100

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One side of Rectangle =5, given

Other side of Rectangle = x

Side of Square =y

Area of Rectangle =5*x

Area of Square = y2

5x:y2 =1:4

y2 =20x

Now,

Perimeter Of Rectangle= 2 (5+x)

Perimeter Of Square = 4y

2 (5+x) : 4y=1:2 ,

5+x=y

Squaring both side

25+x2 +10x =y2

25+x2 +10x =20x

x2 -10x+25=0

x=5

y2=20x =20*5 =100

Area = y2 =100