Question

the adjacent sides of parallelogram are 4a, 3a. the angle b/w them is 60, then one of the diagonal of the parallelogram? ​

Answer 1

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Two adjacent sides and the respective diagonal makes a triangle and here, we have the length of two sides and the angle between them..

By using cosine law,

(Refer to the attachment)

➙ d² = (4a)² + (3a)² - 2×4a×3a×cos 60°

➙ d² = 16a² + 9a² - 24a² × 1/2

➙ d² = 25a² - 12a²

➙ d² = 13a²

➙ d = √(13a²)

➙ d = a√13

➙ d ≈ 3.61 a (Ans)

One of the diagonal will have length 3.61a. Similarly you can find the length of other diagonal with the included angle as 120°.

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Answer 2

Answer:

Verified Answer

Two adjacent sides and the respective

diagonal makes a triangle and here, we

have the length of two sides and the angle

between them..

By using cosine law,

(Refer to the attachment)

d² = (4a)² + (3a)² - 2×4a×3axcos 60°

d² = 16a² +9a² - 24a² x 1/2

X

→ d² = 25a² - 12a²

→ d² = 13a²

→ d = √(13a²)

→ d = a√13

→ d = 3.61 a (Ans)

One of the diagonal will have length 3.61a.

Similarly you can find the length of other

diagonal with the included angle as 120°.