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If the parallelogram has a perimeter of 176, find the area.

+1 vote
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The length of the altitudes from a vertex of the parallelogram to the other two sides is 10 and 12.

Area of parallelogram

If the parallelogram has a perimeter of 176, find the area.

posted Oct 1, 2014 by Varuna Magar

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1 Solution

+4 votes

Let x be the angle opposite to 12 and 10.
Smaller side be a
Larger side be b
The perimeter is 2a + 2b = 176, so a + b = 88.
Since Sin x = 10/a and Sin x = 12/b
12/b = 10/a
12a = 10b
a = 5b/6
Thus, a + b = 88
5b/6 + b = 88
11b/6 = 88
b/6 = 8
b = 48
10 is the altitude since it's perpendicular to a base.
Therfore Area = (10)(48) = 480 sq. units

solution Jan 27, 2015 by Jaspalsingh Parmar
Well done.Superb solved



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