Question

Circle O is inscribed in triangle KLM. KC = 3 units, MB = 5 units and KL = 14 units. Find the perimeter of triangle KLM.
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Answer 1

By virtue of the circle inscribed in a triangle, it doesn't imply that it has to be a perfect triangle. It can also mean that the triangle has 2 equal-length sides with another longer / shorter side.

Based on your question with the limited information, my best assumption is that KL is the longer/shorter side and KM and ML is equal in length.

P (perimeter) = KL + KM + ML

since KM = KC + KM and ML = MB + BL,

P = KL + KC + CM + MB + BL

since KM & ML is equal in length and KC and MB denotes the different portion of the 2 equal sides, KC = BL and MC = MB

P = 14 + 3 + 5 + 5 + 3
= 30

Answer 2

THANK YOU!

Answer 3

welcome.

Answer 4

I'm afraid slnkktn's answer is incorrect - assuming that 2 sides of the triangle are equal is an invalid assumption. We solve this problem by using the property that in a triangle with an inscribed circle, the lengths of the segments from each vertex to each of the two neighboring intersections of the triangle and the circle are equal. Ie, KA = KC, MB = MC, and LA = LB. We know that KL = 14, and that KA = KC = 3. Thus, LA = 14-3 = 11. Thus LB = 11. We also know that MB = MC = 5. Thus KL = 14, LM = 11 + 5 = 16, and KM = 3 + 5 = 8. Then the perimeter is 14 + 16 + 8 = 38.