What is the ratio of (EF+FG+GH+HE) and (AD+DC+CB+BA)?

ABCD is a parallelogram and the diagonals AC and BD intersect at ‘O’. If E, F, G and H are the midpoints of AO, DO, CO and BO respectively, then what is the ratio of (EF+FG+GH+HE) and (AD+DC+CB+BA)?

  1. 1:2
  2. 2:3
  3. 3:4
  4. 4:5
Anurag Mishra Professor Asked on 17th December 2015 in Maths.
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1 Answer(s)

Answer:  (1) 1: 2

Solution:-
According to the question,
 In the diagram-

RE: What is the ratio of (EF+FG+GH+HE) and (AD+DC+CB+BA)?


In triangle AOD,
AD II EF  and F , F are the midpoint of OA and OD
Then EF = AD/2

Similarly, FG =AB/2, HG = BC/2 & EH = CD/2

Then (EF + FG + GH + HE ) = (AD + DC + CB + BA)/2

 (EF + FG + GH + HE)/ (AD + DC + CB + BA) = 1/2

So, the ratio of (EF + FG + GH + HE) and (AD + DC + CB + BA) is 1: 2.

Hence, the correct answer is option (1) 1: 2. 

Anurag Mishra Professor Answered on 17th December 2015.
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