P(5,6) Q(1,5) R(2,1) and S(6,2) are the vertices of square PQRS. A(3,11/2) B(3/2,3) C(4,3/2) D(11/,4) are the mid points of PQ QR RS and SP respectively. Find the ratio of areas of two squares.
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PQRS is square
first we find one side of square,
PQ=√{(5-1)^2+(6-5)^}
=√17 unit
now,
area of square PQRS=(side length) ^2
=(√17)^2=17 sq unit
again,
side of square ABCD=√{(3-3/2)^2+(11/2-3)^2}
=√{(3/2)^2+(5/2)^2}=√(17/2) unit
now,
area of ABCD square=(side length) ^2
=(√(17/2))^2=17/2
now,
ratio = 17/(17/2)=2
hence ratio is 2:1
first we find one side of square,
PQ=√{(5-1)^2+(6-5)^}
=√17 unit
now,
area of square PQRS=(side length) ^2
=(√17)^2=17 sq unit
again,
side of square ABCD=√{(3-3/2)^2+(11/2-3)^2}
=√{(3/2)^2+(5/2)^2}=√(17/2) unit
now,
area of ABCD square=(side length) ^2
=(√(17/2))^2=17/2
now,
ratio = 17/(17/2)=2
hence ratio is 2:1
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