Question

27. in the rectangle ABCD, AB = 12 cm
BC=7cm. P and R are mid-points of AB and CD.
AS=BQ=2.5. Find the perimeter of PQRS.​

Answer 1

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Answer 2

28 cm

Step-by-step explanation:

First, BC-BQ =AD-AS = 7-2.5 = 4.5 cm

Applying Pythagoras theorem in ∆APS, ∆PBQ, ∆SDR, ∆QRC, We get,

$SP = \sqrt{ {6}^{2} + {2.5}^{2} } = \sqrt{36 + 6.25} = \sqrt{42.25} = 6.5 \: cm$

$PQ = \sqrt{ {6}^{2} + {2.5}^{2} } = \sqrt{36 + 6.25} = \sqrt{42.25} = 6.5 \: cm$

$SR = \sqrt{ {6}^{2} + {4.5}^{2} } = \sqrt{36 + 20.25} = \sqrt{56.25} = 7.5 \: cm$

$QR= \sqrt{ {6}^{2} + {4.5}^{2} } = \sqrt{36 + 20.25} = \sqrt{56.25} = 7.5 \: cm$

Therefore, Perimeter of PQRS = Sum of all sides

= SP + PQ + SR + QR

= 6.5 cm + 6.5 cm + 7.5 cm + 7.5 cm

= 28.00 cm

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