The parallel sides of a trapezoid are 3 cm and 9 cm. the non- parallel sides are 4 cm and 6 cm. a line parallel to the bases divides the trapezoid into two trapezoids of equal perimeters. The ration in which each of the non-parallel sides is divided is

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3 : 1

3 : 2

4 : 3

4 : 1

answer is C.

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Detailed Solution

$\begin{array}{l} peri [APQD] = peri [BCQP] \\ 6 K + PQ + 4 K + 3 = 6 - 6 K + 9 + 4 - 4 K + PQ \\ 10 K + 3 = 19 - 10 K \\ 20 K = 16 \\ K = 0 .8 \\ AP : PB = 6 (0 .8) : 6 - 6 (0 .8) = 4 .8 : 1 .2 = 4 : 1 \\ DQ : QC = 4 K : 4 - 4 K = 3 .2 : 0 .8 = 4 : 1 \end{array}$

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