Triangle Median Problem: Find the Ratio of BC to DC

Question

In front of you the next triangle:

Given AD median in the triangle.

Find the ratio of the length of the side BC and the length of DC.

Video Solution

Solution Steps

00:00 Determine the ratio between BC and DC

00:03 The entire side equals the sum of its parts

00:18 The segments are equal according to the given data

00:26 Substitute in DC for BD

00:37 Determine the ratio between BC and DC

00:47 Simplify wherever possible

00:51 This is the solution

Step-by-Step Solution

In triangle $ABC$ , $AD$ is a median from $A$ to side $BC$ . By definition, a median divides the opposite side into two equal segments: $BD = DC$ . Therefore, the total length of side $BC$ is the sum of $BD$ and $DC$ , which simplifies to $BC = BD + DC = 2 \times DC$ .

We are tasked with finding the ratio $BC : DC$ . Given that $BC = 2 \times DC$ , we conclude the ratio is $2:1$ .

Therefore, the solution to the problem is $2:1$ .

Answer

2:1

Related Subjects

The Sum of the Interior Angles of a Triangle The sides or edges of a triangle Triangle Height Exterior angles of a triangle Median in a triangle Center of a Triangle - The Centroid - The Intersection Point of Medians All terms in triangle calculation