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The area of square ABCD is 144 sq cm.let PQRS be the square obtained by joining the mid-points of the sides of the square ABCD.find the perimeter and area

of the square PQRS.


Area of square ABCD = 144 sq cm
So, side of square ABCD = 12 cm
Side of the square obtained by joining the midpoints of the ABCD =  \sqrt{ (\frac{side}{2})^2+(\frac{side}{2})^2 }

Therefore, the side of the square PQRS =  \sqrt{ (\frac{12}{2})^2+(\frac{12}{2})^2 } =  \sqrt{72} = 6 \sqrt{2}

Area of square PQRS = (6 \sqrt{2}  )^2 = 72 sq cm

Perimeter = 4 × (6 \sqrt{2}) 24 \sqrt{2} cm
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It can be done pythogras theorem
Its done using pythagoras theorem only. the third step explains the same
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