ABCD is a parallelogram. E is a point on AB such that AE : EB = 1 : 3. F is a point CD such tat CF : FD = 3 : 1. Triangles EFG and EFH are drawn such that points G, H are on AD and BC respectively. What is area of EFGH as a percentage of parallelograms ABCD?

Correct Option - 2


Detailed Solution:

Since AE: EB is same as DF : EF Hence, AD must be parallel to BC

So, area of D EFG is 50percent of area of rectangle ADFE

So, area of D EFH is 50percent of area of rectangle BCDE

Hence, area of EFGH is 50percent of the area of parallelogram ABCD

<div class="photo-widget-full"><div class="figure"><picture><source srcset="" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1754908306phpRKjhJ1.jpeg" alt="" width="146" height="122" loading="lazy"></picture></div><div class="figure"><p><span lang="EN-IN">Since AE: EB is same as DF : EF Hence, AD must be parallel to BC</span></p><p><span lang="EN-IN">So, area of </span><span lang="EN-IN">D</span><span lang="EN-IN"> EFG is 50percent of area of rectangle ADFE </span></p><p><span lang="EN-IN">So, area of </span><span lang="EN-IN">D</span><span lang="EN-IN"> EFH is 50percent of area of rectangle BCDE</span></p><p><span lang="EN-IN">Hence, area of EFGH is 50percent of the area of parallelogram ABCD</span></p></div></div>

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