How much to sacrifice for equality...??

Geometry Level 3

In the given figure ,P and Q are the midpoints of AC and AB. Also PG=GR and HQ=HR. What fraction of area of triangle ABC should be removed so as to make it's area equal to that of triangle PQR ?


The answer is 0.5.

Tanmay Goyal by tanmay goyal , 21, India

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1 solution

Tanmay Goyal
Jan 30, 2015

Using BPT , we see that height of trpezium PCBQ is equal to the height of triangle APQ.

And height of trapezium PGHQ =height of triangle RGH..

SO height of triangle ABC is equal to height of triangle PQR ..

Now a r e a o f t r i a n g l e P Q R a r e a o f t r i a n g l e A B C \frac{area of triangle PQR}{area of triangle ABC} = b h 4 b h / 2 \frac{\frac{bh}{4}}{bh/2}

(Base PQ IS HALF OF BASE BC ,by MIDPOINT THEOREM )

Area to remove =1- 0.5= 0.5 \boxed{0.5}

2 Helpful 0 Interesting 0 Brilliant 0 Confused

how does the height becomes equal in both the cases? pls let me know

Akash Bhandari - 5 years, 7 months ago

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