Pascal questoin: trapezoid's parallel sides are in ratio of

[ejkaminsky]

Ina trapezoid the parallel sides are in the ratio k:1 where k>1. The line segment joining the midpoints of the non-parallel sides divides the trapezoid into two regions whose areas are in the ratio 5:2. What is the value of k?

A) 12
B)5/2
C)13
D)25/5
E)7

 

[TchrWill]

Re: Pascal questoin: trapezoid's parallel sides are in ratio

Ina trapezoid the parallel sides are in the ratio k:1 where k>1. The line segment joining the midpoints of the non-parallel sides divides the trapezoid into two regions whose areas are in the ratio 5:2. What is the value of k?

A) 12
B)5/2
C)13
D)25/5
E)7

Let a = the short parallel side and ka = the long side.

Then, a(k+1)/2 = the median (the average of the two parallel sides).

The larger area A1 = [ka + a(k+1)/2]/2 = a(3k+1)/4

The smaller area is A2 = [a + a((k+1)]/2

Dividing a1 by a2 yields (3k+1)/(k+3) = 5/2

I suspect you can take it from here.