SOLUTION: What is the area of the Parallelogram ABCD whose adjacent sides are of Length are 12cm and 17cm and one of the diagnol is of 25cm? Also what is the length of Perpendicular BE drawn

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Question 1089898: What is the area of the Parallelogram ABCD whose adjacent sides are of Length are 12cm and 17cm and one of the diagnol is of 25cm? Also what is the length of Perpendicular BE drawn from vertex B on side AD?
Answer by ikleyn(52799) About Me  (Show Source):
You can put this solution on YOUR website!
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Use the law of cosine to find cosine of the angle between the adjacent sides:

25%5E2 = 12%5E2 + 17%5E2 - 2%2A12%2A17%2Acos%28alpha%29  ====>

cos%28alpha%29 = %28625+-+144+-+289%29%2F%28-2%2A12%2A17%29 = -8%2F17.


    In particular, the angle alpha is obtuse.


Then find sin%28alpha%29 = sqrt%281-cos%5E2%28alpha%29%29 = sqrt%281-%28-8%2F17%29%5E2%29 = sqrt%28%28289-64%29%2F289%29 = sqrt%28225%29%2F17 = 15%2F17.


Now, the area of the parallelogram is the product of the dimensions of two adjacent sides by the sine of the concluded angle


Area = 12%2A17%2A%2815%2F17%29 = 12*15 = 180 cm^2.

To find the altitude of the parallelogram, divide its area by the base length.

Solved.