Given: A parallelogram with diagonals equal to 56cm and 34cm. The intersect of the angles is 120^circ. Find the shorter side's length.

Emily-Jane Bray

Emily-Jane Bray

Answered question

2021-03-08

Given:
A parallelogram with diagonals equal to 56cm and 34cm. The intersect of the angles is 120. Find the shorter side's length.

Answer & Explanation

smallq9

smallq9

Skilled2021-03-09Added 106 answers

Suggest the length of the shorter side is x. The 120 angle is opposite to the longer side. So the angle opposite to the shorter side is 180120=60. Now we have a triangle with one side being x, and the two others: 17cm and 28cm, because the diagonals of a parallelogram bisect each other. Use the Law of Cosines to solve this.
x2=282+1722(28)(17)cos60
x2=597
x=597
x24.4 cm
The shorter side is approximately 24.4cm long.

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