The hypotenuse KP of a right-angled triangle KMP is 2√13 cm, and the leg MP is 4 cm. Find the median PС.

univerkov | June 25, 2021 | education

Let MP = 4 cm; hypotenuse KP = 2√13 cm, find the median PC.

1) First, define the second leg: MK = √ (KP ^ 2 – MP ^ 2) = √ (2√13 ^ 2 – 4 ^ 2) = √ (52 – 16) = √36 = 6 (cm).

2) The median PC divides the hypotenuse of KM in half, which means that KS = CM = KM / 2 = 6/2 = 3 cm.

3) Now consider also a right-angled triangle PCM, CP at 25 = 25 = 5, we find the hypotenuse by the formula:

CP ^ 2 = CM ^ 2 + MP ^ 2; CP ^ 2 = 3 ^ 2 + 4 ^ 2 = 9 + 16 = 25 (cm). Whence CP = √25 = 5 (cm).

Answer: median CP = 5cm.

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