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09 Dec 2021, 04:00
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
53% (02:42) correct
47%
(01:46)
wrong
based on 15
sessions
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From a triangle ABC with sides of lengths 40 ft, 25 ft and 35 ft, a triangular portion GBC is cut off where G is the centroid of ABC. The area, in sq ft, of the remaining portion of triangle ABC is
A) 225√3
B) 500/√3
C) 275/√3
D) 250/√3
E) 300
Are You Up For the Challenge: 700 Level Questions
A) 225√3
B) 500/√3
C) 275/√3
D) 250/√3
E) 300
Are You Up For the Challenge: 700 Level Questions
09 Dec 2021, 06:53
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Bunuel
Correct answer B
In order to find the area of a triangle with 3 sides, we use Heron's formula which says if a, b, and c are the three sides of a triangle, then its area is,
Area = √[s(s-a)(s-b)(s-c)]
Here, "s" is the semi-perimeter of the triangle, i.e., s = (a + b + c)/2.
s=50, (s-a)=10, (s-b)=25, (s-c)=15
Area of triangle ABC comes out to be 250√3
Now here's where the fun part comes- Point G is the centroid and hence it divides the median into the ratio of 2:1; hence traingles ABC and GBC are also in the same ratio i.e. 2:1 since they have the same base BC
So the area of the remaining portion of the triangle is 250√3 * (2/3) = 500/√3
The correct answer is B. Cheers
09 Dec 2021, 07:25
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Bunuel
Just in case any test taker reading this question becomes concerned about the geometry they've studied, you don't need to know what the "centroid" of a triangle is for the GMAT.
