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Question

# A boy is designing a diamond shaped kite, as shown in the figure where AE=16 cm,EC=81 cm. He wants to use a straight cross bar BD. How long should it be?

A
27 cm
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B
72 cm
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C
48 cm
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D
56 cm
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Solution

## The correct option is B 72 cmHere ∠B and ∠D both are 90oNow, in right angle △AEB,(AB)2=(AE)2+(BE)2 [ By Pythagoras theorem ]⇒ (AE)2=(AB)2−(BE)2⇒ (16)2=(AB)2−(BE)2 ---- ( 1 )And in right angled △BEC,⇒ (BC)2=(EC)2+(BE)2 [ By Pythagoras theorem ]⇒ (EC)2=(BC)2−(BE)2⇒ (81)2=(BC)2−(BE)2 ----- ( 2 )Adding equation ( 1 ) and ( 2 ),⇒ (16)2+(81)2=(AB)2+(BC)2−(BE)2−(BE)2 ---- ( 3 )Now in right angle △ABC,⇒ (AB)2+(BC)2=(AC)2=(16+81)2=(97)2Putting this in equation (3) we get,⇒ 2(BE)2=(97)2−[(16)2+(81)2]⇒ 2(BE)2=9409−(256+6561)⇒ 2(BE)2=2592⇒ (BE)2=1296∴ BE=36cm∴ BD=2BE=2×36=72cm

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