How to do this question

Length of the shorter diagonal is 8.68 cm.

Step-by-step explanation:

Length of the side AB = 11 cm

Length of side BC = 5 cm

Angle between these sides, m∠ABC = 50°

By cosine rule in ΔABC,

AC² = AB² + BC² - 2AB.BC.cos B

AC² = (11)² + 5² - 2(11)(5)cos50°

AC² = 121 + 25 - 70.71

AC = √(75.29)

AC = 8.68 cm

By the property of parallelogram,

m∠B + m∠C = 180° [Interior consecutive angles]

50° + m∠C = 180°

m∠C = 130°

Similarly, In ΔBCD,

BD² = BC² + CD² - 2BC.CD.cos130°

BD² = (5)² + (11)² - 2(5)(11)cos130°

BD² = 25 + 121 + 70.71

BD² = 216.71

BD = 14.72 cm

Therefore, length of the shorter diagonal will be 14.72 cm.

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