In the isosceles triangle MKP with the base of the KP, the median MA is drawn. The perimeter of the MKP is 38 cm

univerkov | July 21, 2021 | education

In the isosceles triangle MKP with the base of the KP, the median MA is drawn. The perimeter of the MKP is 38 cm, and the perimeter of the APM is 30 cm. Find the length of the median MA.

Since the triangle is isosceles, then KM = MP, and since MA is the median, then KA = PA.

The perimeter of the triangle is Ркмр = КМ + МР + КР = 38 cm.

The perimeter of the triangle Rarm = MP + AP + MA = 30 cm.

The perimeter of the triangle Rakm = KM + AK + MA = 30 cm.

Let’s add the last two equations.

MP + AP + MA + KM + AK + MA = 60.

Since AK + AP = KP, then:

(KM + MP + KP) + 2 * MA = 60.

The expression in brackets is the perimeter of the KMP triangle.

38 + 2 * MA = 60.

MA = (60 – 38) / 2 = 11 cm.

Answer: The median length is 11 cm.

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