Find the length of line BC in the triangle ADC with line DB being the median of the triangle.

Question

AC = 70 and line DB
is the median of the triangle. Please show all work in order to get credit for this problem.

Answer 1

In triangle ADC, DB is the median, which means it divides the side AC into two equal parts.

Let's label the point where DB intersects AC as point E. So, AE = EC = 70/2 = 35.

Now, we have a right-angled triangle ADE. We can use the Pythagorean theorem to find the length of DE.

Let's label the length of DE as x.

Using the Pythagorean theorem, we have:

AD^2 + DE^2 = AE^2

Since AD = 70 and AE = 35, the equation becomes:

70^2 + x^2 = 35^2

4900 + x^2 = 1225

x^2 = 1225 - 4900

x^2 = 3675

x = √3675

x ≈ 60.62

So the length of DE is approximately 60.62.

Since DB is the median, it divides AC into two equal parts. So, EC = DE = 60.62.

Therefore, the length of line BC is 2 times the length of EC.

BC = 2 * EC

BC = 2 * 60.62

BC ≈ 121.24

Thus, the length of line BC is approximately 121.24 units.