A line EF parallel to the base, divides the trapezoid into two trapezoids of equal perimeters. Calculate the ratio in which each of the non-parallel sides is divided.
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Solution
Let FA=x⇒FE=6−x
And CB=Y⇒DC=4−y
Perimeter of trapezium ABCF
= 9 + y + FC + x
Perimeter of trapezium FCDE
= FC + 4 – y + 3 + 6 – x
= FC + 13 –x – y ⇒ 9 + y + FC + x = FC + 13 – x – y ⇒9+y+x=13−x−y 2(x+y)=13−9=4⇒x+y=2....(1)
But 6−xx=4−yy⇒y=23x
From eq (1) 2x3+x=2⇒x=65 ∴ Required ratio = EF:FA [or DC:CB] =6−xx=6−6565=246=41=4:1