Multiple choice

Directions: Solve the following question and mark the best possible option. 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

  1. 225 3

  2. 500/ 3

  3. 275/ 3

  4. 250/ 3
Reveal answer Fill a bubble to check yourself
B Correct answer
AI explanation

Using Heron's formula for triangle ABC with sides 40, 25, and 35, the semi-perimeter s is (40 plus 25 plus 35) divided by 2, which equals 50. The area is the square root of (50 times (50 minus 40) times (50 minus 25) times (50 minus 35)), yielding the square root of (50 times 10 times 25 times 15), which simplifies to 250 times the square root of 3. The median of a triangle divides it into two triangles of equal area, so the three medians divide the triangle into six smaller triangles of equal area. The triangular portion GBC consists of two of these smaller triangles, meaning its area is one-third of the total area of triangle ABC. The area of the remaining portion is two-thirds of the total area, which is two-thirds of 250 times the square root of 3, yielding 500 divided by 3 times the square root of 3.

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