Multiple choice

If medians of a triangle have lengths 18 cm, 24 cm and 30 cm, then what is the area (in cm2) of the triangle?

  1. 251

  2. 244

  3. 288

  4. 360
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Area of a triangle with medians m1, m2, m3 is (4/3) * sqrt(s(s-m1)(s-m2)(s-m3)) where s is the semi-perimeter of the medians. s = (18+24+30)/2 = 36. Area = (4/3) * sqrt(36 * 18 * 12 * 6) = (4/3) * sqrt(46656) = (4/3) * 216 = 288.

AI explanation

The area of a triangle formed by its three medians is three-fourths of the area of the original triangle. First, find the area of the triangle with sides 18 cm, 24 cm, and 30 cm. Since 18 squared plus 24 squared equals 30 squared, this median triangle is right-angled, so its area is one half times 18 times 24, giving 216 square cm. The area of the original triangle is four-thirds of this median triangle's area: (4 divided by 3) times 216 equals 288 square cm.

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