In triangle ABC, the sides AB and BC are equal and the median BD is 4 cm.

| September 9, 2021 | education

In triangle ABC, the sides AB and BC are equal and the median BD is 4 cm. Find the perimeter of the triangular ABC if the perimeter of triangle ABD is 12 cm

Since triangle ABC is isosceles, the median BD is also the bisector of angle B. Triangle ABD is equal to triangle BCD, since AB = BC, side BD is common, and angle ABD = CBD. Triangles are equal on both sides and the angle between them. Then the perimeter of the triangle BCD is equal to the perimeter of ABD. Let’s find the sum of the perimeters of the triangles ABD and BCD.

Ravd + Rvsd = AB + BD + AD + BC + CD + BD = 12 + 12 = 24 cm.

AD + CD = AC.

Then Ravd + Rvsd = (AB + BC + AC) + 2 * BD = 24 cm.

In brackets, the perimeter of the triangle ABC, then:

Ravs = 24 – 2 * BD = 24 – 2 * 4 = 16 cm.

Answer: The ABC perimeter is 16 cm.



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