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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?

A) 96

B) 85

C) 72

D) 105

E) 112

Dec 19, 2017

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Let one of the parallel sides   = x......so the other is 22-x

And  the length of the  midline  = sum of the parallel sides / 2  =  22/2  = 11

Let the area of the smaller part  =  (h/2)(11 + 22 -x)  = (h/2)(33 - x)

Let the area of the larger part  = (h/2)(11 + x)

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

(7/4)*(h/2)*(33-x)  = (h/2)*(11+ x)

(7/4) (33 - x )   =  (11 + x)

7(33 - x)  = 4(11 + x)

231  - 7x   =  44 + 4x       add 7x to both sides, subtract 44 from both sides

187  =  11x         divide both sides by 11

17  = x

So.....one parallel base  = 17  and the other is  22-17  = 5

And their product  = 17 * 5   =  85   Dec 20, 2017