Multiple choice

Construct a triangle ABC in which BC = 5cm, and median AD through A is of length 3.5cm. Also, determine the length of the altitude drawn from A on the side BC

  1. $5$
  2. $4$
  3. $3$
  4. $7$
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C Correct answer
AI explanation

Since point D is the midpoint of BC, the given median AD = 3.5 cm divides the triangle into two triangles with equal bases of 5/2 = 2.5 cm. In a triangle where two sides are 3.5 cm and 2.5 cm, the Pythagorean triple 3-4-5 scaled down by half applies, creating a right-angled triangle with a hypotenuse of 3.5, a base of 2.5, and a perpendicular of 3. Thus, the length of the altitude drawn from A on the side BC is 3 cm. The length of the altitude is 3.

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