Question

the length of the altitudes from a vertex of the parallelogram to the other two sides are 10 and 12. if the parallelogram has a perimeter of 176, find the area.

Answer 1

480

Explanation:

Let x be the angle opposite to 12 and 10.

The smaller side is A

The larger side is 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

So,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.

Area = (10)(48) = 480 sq. units