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In the adjoining figure, ABCD is a rectangle in which AB = 6 cm and AD = 8 cm. If P and Q are mid-points of the sides BC and CD respectively, then the length of PQ is

  1. 7 cm

  2. 5 cm

  3. 4 cm

  4. 3 cm

In the figure, ABCD is a rectangle AB = 6 cm and AD = 8 cm. If P and Q are mid-points of BC and CD, then the length of PQ is? Mid-point Theorem, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

Mid-point Theorem

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Answer

Length of diagonal (BD) of ABCD = AB2+AD2=62+82=36+64=100\sqrt{AB^2 + AD^2} = \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10 cm.

In △BCD,

P is midpoint of BC and Q is midpoint of CD.

PQ || BD and PQ = 12\dfrac{1}{2}BD = 12\dfrac{1}{2} x 10 = 5 cm.

Hence, Option 2 is the correct option.

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