We have a triangle ABC and a point K on segment BC such that AK is an altitude to triangle ABC. If AK = 6, BK = 8, and CK = 7, and then what is the perimeter of the triangle?
We have a triangle ABC and a point K on segment BC such that AK is an altitude to triangle ABC. If AK = 6, BK = 8, and CK = 7, and then what is the perimeter of the triangle?
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Perimeter P = √(62 + 82) + 15 + √(62 + 72)
+128460 Note that we have two right triangles formed by AK
One is triangle BAK and the other is CAK
BC = BK + CK =15
Usinfg the Pythagorean Theorem
BA = sqrt ( BK^2 + AK^2) = sqrt ( 8^2 + 6^2) = sqrt ( 100) = 10
And
CA =sqrt ( CK^2 + AK^2) = sqrt ( 7^2 + 6^2) = sqrt (85)
So....the perimeter is BC + BA + CA = 15 + 10 sqrt (85) = 15 + 10 sqrt (85)
