The adjacent sides of a parallelogram are 30 cm and 20 cm. The length of one of the diagonal is 40 cm. What is the length of the other diagonal? A) 60 cm b) 10 10 cm c) 20 5 cm d) 8 30 cm
Answers
Given : adjacent sides of a parallelogram are 30 cm and 20 cm. The length of one of the diagonal is 40 cm
To find : The length of one of the diagonal is 40 cm.
Solution:
The adjacent sides of a parallelogram are 30 cm and 20 cm
Diagonal length = 40 cm
Adjacent sides & Diagonal form a triangle
Applying cosine formula
40² = 30² + 20² - 2*30*20Cosα
=> 1600 = 900 + 400 - 1200Cosα
=> Cosα = -300/1200
=> Cosα = -1/4
=> α = Cos⁻¹(-1/4)
sum of adjacent angle of parallelogram = 180°
Hence Other angle = 180° - α
Cos(180° - α) = - Cosα = - Cos(Cos⁻¹(-1/4)) = - (-1/4) = 1/4
other diagonal² = 30² + 20² - 2*30*20(1/4)
=> other diagonal² = 900 + 400 -300
=> other diagonal²= 1000
=> other diagonal = 10√10 cm
option b is correct : other diagonal = 10√10 cm
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