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

jonathanxu999
Dec 19, 2017

#1**+1 **

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

CPhill
Dec 20, 2017