Asked by bob
Triangle D F E is shown. Lines are drawn from each point to the opposite side to form right angles. The lines intersect at point K. All side lengths are congruent.
[Figure may not be drawn to scale]
In triangle DFE, KJ = 50 units. What is the length of segment EK?
25 units
50 units
100 units
150 units
All Answers 1
Answered by
GPT-5 mini
AI
100 units
Reason: In an equilateral triangle of side a the altitude = a√3/2. The intersection K is 2/3 of the way down the altitude from a vertex, so KJ (distance from K to a side) = a√3/6 = 50. Hence a = 100√3. The distance from K to a vertex (EK) = 2/3 of the altitude = a√3/3 = a/√3 = 100.
Reason: In an equilateral triangle of side a the altitude = a√3/2. The intersection K is 2/3 of the way down the altitude from a vertex, so KJ (distance from K to a side) = a√3/6 = 50. Hence a = 100√3. The distance from K to a vertex (EK) = 2/3 of the altitude = a√3/3 = a/√3 = 100.
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