SOLUTION: The sum of the two parallel sides of a trapezoid is 22 cm. The segment that connects the mid points of the two non-parallel sides divides the area of the trapezoid into two parts,

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Question 1150160: The sum of the two parallel sides of a trapezoid is 22 cm. The segment that connects the mid points of the two non-parallel sides divides the area of the trapezoid into two parts, in a ratio of 4:7. What is the product of the lengths of the two parallel sides?
Answer by greenestamps(13195) About Me  (Show Source):
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Let the length of the line segment joining the midpoints of the two non-parallel side be x. Then let the lengths of the two bases be 11-x and 11+x.

The trapezoid has been divided into two trapezoids, in which the ratio of the areas is 4:7.

Let the height of each of those two trapezoids be h (so the height of the original trapezoid was 2h).

The area of a trapezoid is the height, multiplied by the average of the two bases. Given the ratio of the areas of the two trapezoids is 4:7, we have

%28h%28%2811-x%2B11%29%2F2%29%29%2F%28h%28%2811%2B11%2Bx%29%2F2%29%29+=+4%2F7

%2822-x%29%2F%2822%2Bx%29+=+4%2F7
88%2B4x+=+154-7x
11x+=+66
x+=+6

The lengths of the two parallel sides are 11-x = 5 and 11+x = 17; the product of the lengths of the two parallel sides is 5*17 = 85.