RudeyboyZ wrote:
Could you guys explain it a little in detail as to why is statement 1 sufficient. I did not get it.
Warm Regards,
Rudraksh.
Dear
RudeyboyZPlease refer to the image below. It represents the information that we were given in the Question Statement and in St. 1.Also, if AB = 8x and BC = 15x, can you calculate AC? Sure, using Pythagoras Theorem, you know that it's 17x.
Now, area of triangle ABC =\(\frac{1}{2}*AB*BC\) = \(\frac{1}{2}*8x*15x\)
But, suppose you take the base as AC. Then, what is the height? BD. And St. 1 tells us that BD = 120
So, the area of triangle ABC can also be written as = \(\frac{1}{2}*BD*AC\) = \(\frac{1}{2}*120*17x\)
By equating the two expressions for area of triangle ABC, you can find the value of x and therefore, you can find a unique value of the area of triangle ABC. So, St. 1 is sufficient.
Note that I could analyze Statement 1 till its logical conclusion because:
1. I drew a neat diagram that represented all the pieces of information that were given in Question statement + St. 1 and also the information that I had inferred (AC = 17x, using Pythagoras Theorem)
2. I was able to mentally rotate the triangle ABC such that AC became its base. By doing so, I could see that the area of triangle ABC can also be written as \(\frac{1}{2}*BD*AC\). This ability to mentally rotate a given image comes in handy in many questions.
Here's an official question that involves rotation of a triangle:
https://gmatclub.com/forum/in-the-figure-above-triangle-abc-is-equilateral-and-point-143496.htmlHope this helped!
Japinder