In the isosceles triangle MKP (MK = KP), the bisector KE was drawn. Find its length if the perimeter
| September 16, 2021 | education
In the isosceles triangle MKP (MK = KP), the bisector KE was drawn. Find its length if the perimeter of the MKP triangle is 72cm, and the perimeter of the MKE triangle is 48cm
Since the triangle is isosceles, then KM = KP, and since KE is the median, then ME = PE.
The perimeter of the triangle is Ркмр = КМ + МР + КР = 72 cm.
The perimeter of the Rerk triangle = KP + EP + KE = 48 cm.
The perimeter of the triangle Rekm = KM + EM + KE = 48 cm.
Let’s add the last two equations.
KP + EP + KE + KM + EM + KE = 96.
Since ME + PE = MР, then:
(KM + KР + MР) + 2 * KE = 96.
The expression in brackets is the perimeter of the CMР triangle.
72 + 2 * KE = 96.
KE = (96 – 72) / 2 = 12 cm.
Answer: The median length is 12 cm.
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