Multiple choice

In a triangle ABC, AD is the bisector of ∠BAC. If AB = 12 cm, BD = 10 cm and DC = 5 cm, then what is the perimeter of the triangle?

  1. 30 cm

  2. 31 cm

  3. 33 cm

  4. 35 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

By the Angle Bisector Theorem, AB/AC = BD/DC. Substituting the values, 12/AC = 10/5, which gives AC = 6 cm. The perimeter is AB + AC + (BD + DC) = 12 + 6 + 15 = 33 cm.

AI explanation

By the angle bisector theorem, we have AB / AC = BD / DC, so 12 / AC = 10 / 5, which gives AC = 6 cm. The perimeter of triangle ABC is the sum of its sides: 12 + 6 + 10 + 5 = 33 cm. The result is 33 cm.

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