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Draw a parallelogram $A B C D$ within which $A B = 6.5 cm, A D = 4.8 cm$ within which and $∠ B A D = 70 ° .$ and

What are the lengths of its diagonals?

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8.5 cm and 9.2 cm

9.2 cm and 8.3 cm

9.2 cm and 6.6 cm

9.4 cm and 6.6 cm

answer is C.

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Detailed Solution

We have been given a parallelogram

A B C D

within which

A B = 6.5 cm, A D = 4.8 cm

and

∠ B A D = 70 ° .

Construction:
Draw AD up to 4.8 cm.
Make an angle of

70 o

at A and cut an arc of 6.5 cm. Name it B.
Cut an arc of 4.8 cm from B and 6.5 cm from D. Name it C.
Join AB, BC, CD and DA.
Measuring the diagonals AC and BD, we get AC up to 9.2 cm and BD up to 6.6 cm.
Question Image

We have successfully constructed the diagram and the lengths of the diagonals are 9.2 cm and 6.6 cm.
Hence option (3) is correct.

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