Answer:
AK = CN = 9.6 cm
BN = 8 cm
Step-by-step explanation:
AC is the base of the isosceles triangle, so N is the midpoint of AC. CN is 6 cm, so the Pythagorean Theorem tells us the altitude BN is
... BN = √(BC² -CN²) = √(100 -36) = 8 . . . . cm
The area of the triangle is ...
... Area = (1/2)(AC)(BN) = (1/2)(12 cm)(8 cm) = 48 cm²
The other altitudes (AK, CM) are to sides of length 10, so they can be found from the area formula as ...
... 48 cm² = (1/2)·altitude·(10 cm)
... 48 cm²/(5 cm) = altitude = 9.6 cm
Thus we have BN = 8 cm, AK = CM = 9.6 cm.
