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Question

The area of a parallelogram is 30 square centimetres. One of its sides is 6 centimetres and one of its angles is 60°. What is the length of its other side?

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Solution

Let ABCD be the given parallelogram.

DC = 6 cm and ADC = 60°

Area of parallelogram ABCD = 30 cm2

Construction: Draw AE perpendicular to DC.

Area of a parallelogram = Base × Height

30 cm2 = 6 cm × AE

AE =

Using angle sum property in ΔAED:

ADE + DEA + EAD = 180°

60° + 90° + EAD = 180°

150° + EAD = 180°

⇒ ∠EAD = 180° 150° = 30°

Thus, the angles of ΔAED are 30°, 60° and 90°.

Therefore, the ratio of the lengths of the sides of ΔAED is 1::2.

Thus, the length of other side of the parallelogram is cm.

Note: We can also draw the figure by taking ADE = 60° and AD = 6 cm.


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