Question

In △ABC, the median from A is perpendicular to the median from B. If BC=7 and AC=6, find AB.

Answer 1

In triangle ABC, we can find AB by using the medians and applying Pythagoras' theorem.

Step-by-step explanation:

In triangle ABC, the median from A is perpendicular to the median from B. Let M be the midpoint of BC and N be the midpoint of AC. Since the medians of a triangle divide each other in a 2:1 ratio, we can find that BN = 3. By Pythagoras' theorem, AM = √(AB^2 - BM^2) and AN = √(AB^2 - MN^2). Since the medians are perpendicular, we can set up the equation AM^2 + AN^2 = MN^2, substitute the values we know, and solve for AB.

Learn more about Finding the length of a side in a triangle using medians