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3 years ago

Given: △ABC, AB=BC=10 cm,

Mathematics

1 answer:

slava [35]3 years ago

7 0

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.

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