Find the length of BC. AC = 70 and DB is the median of the triangle. Please show all work in order to get credit for this problem
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To solve this problem, we need to understand a key characteristic of medians in a triangle:
When a median is drawn in a triangle, it divides the triangle into two smaller triangles that have equal area. A median connects a vertex of the triangle to the midpoint of the opposite side, meaning that DB is the median from D to side AC; hence B is the midpoint of AC. This also implies that AB = BC since B is the midpoint.
Given AC = 70, the midpoint B divides AC into two equal segments:
AB = BC = AC / 2
BC = 70 / 2
BC = 35
The length of segment BC is 35 units.