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# The sum of the two parallel sides of a trapezoid is 22 cm

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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?

Dec 9, 2017

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The  midpoint segment is  (1/2)  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/2

Call one of the base lengths x....and the other 22 - x

So call  the area of the smaller trapezoid  =  h ( 11 + x)/2

And the area of the larger trapezoid  = h (11 + [22 - x]) /2  =  h (33 - x)/2

And

(7/4) area of the smaller  = area of the larger....so....

(7/4)h (11 + x) /2  = h(33 - x) /2

(7/4) (11 + x)  =  33 - x

77 + 7x  =  132 - 4x

11x  = 209

x = 19 cm

And the other base  = 22 - 19  = 3cm

So...the product of the bases  = 19 * 3  = 57

Dec 9, 2017
edited by CPhill  Dec 9, 2017
edited by CPhill  Dec 9, 2017