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

Algebra ->  Length-and-distance -> SOLUTION: The sum of the two parallel sides of a trapezoid is 22 cm. The segment that connects the midpoints of the two non-parallel sides divides the area of the trapezoid into two parts, i      Log On


   

Question 1131094: The sum of the two parallel sides of a trapezoid is 22 cm. The segment that connects the midpoints 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 MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

The sum of the two parallel sides of a trapezoid is 22 cm.
=> the midpoint segment is %281%2F2%29+ sum of the parallel bases = 11cm

So, the height of the trapezoid => +h
And the height of each separate trapezoid created by the midpoint line = h%2F2
Call one of the base lengths x, and the other 22+-+x
So call the area of the smaller trapezoid A%5B1%5D=++h+%28+11+%2B+x%29%2F2
And the area of the larger trapezoid A%5B2%5D=+h+%2811+%2B+%2822+-+x%29%29+%2F2++=++h+%2833+-+x%29%2F2
given A%5B1%5D%2FA%5B2%5D=4%2F7
so,
+%28h+%28+11+%2B+x%29%2F2%29%2F%28h+%2833+-+x%29%2F2%29=4%2F7


++%28+11+%2B+x%29%2F%2833+-+x%29=4%2F7.....cross multiply
++7%28+11+%2B+x%29=4%2833+-+x%29
++77+%2B+7x=132+-+4x
++4x+%2B+7x=132+-+77
++11x=55
++x=5cm-> one base
And the other base =>+22+-+5++=+17cm
So,the product of the bases is 5+%2A17++=+85