Multiple choice

Choose the correct answers from the alternatives given. If length of three medians of a triangle are respectively $9$ cm, $12$ cm and $15$ cm then what is the area of the triangle in $cm^2$?

  1. $48$
  2. $72$
  3. $96$
  4. $36$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The area of a triangle with medians m1, m2, m3 is (4/3) * sqrt(s(s-m1)(s-m2)(s-m3)), where s = (m1+m2+m3)/2. Here s = (9+12+15)/2 = 18. Area = (4/3) * sqrt(18 * 9 * 6 * 3) = (4/3) * sqrt(2916) = (4/3) * 54 = 72.

AI explanation

The area of a triangle can be found from its medians using the formula that the area is four-thirds the area of the triangle formed by the medians. The medians 9, 12, and 15 form a right triangle because they satisfy the Pythagorean theorem. The area of this right triangle is one-half times 9 times 12, resulting in 54. Multiplying this by four-thirds gives the original triangle's area as 72 square cm.

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