Question

In triangle abc, ab = 8, bc = 10, and ac = 12. let m,n, and k be the midpoints of the sides of triangle abc. find the length of each side of triangle mnk

Answer 1

To find the lengths of the sides of triangle MNK, where M, N, and K are the midpoints of triangle ABC, divide the lengths of the sides of ABC by 2. The resulting lengths are 6 for MN, 4 for NK, and 5 for MK.

Step-by-step explanation:

The student asked about finding the lengths of the sides of triangle MNK when M, N, and K are the midpoints of the sides of triangle ABC, with side lengths AB = 8, BC = 10, and AC = 12. We can apply the properties of a triangle and its mid-segment to solve this problem. The mid-segment of a triangle is the segment that connects the midpoints of two sides of the triangle, and its length is half the length of the third side of the triangle.

Therefore, using this property, we can find the length of each side of triangle MNK as follows:

• The length of side MN is half the length of side AC, so MN = AC / 2 = 12 / 2 = 6.
• The length of side NK is half the length of side AB, so NK = AB / 2 = 8 / 2 = 4.
• The length of side MK is half the length of side BC, so MK = BC / 2 = 10 / 2 = 5.

Thus, the sides of triangle MNK are 6, 4, and 5 units in length, respectively.