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

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

+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

Well done.Superb solved

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