Question

In triangle ABC , A-B-C and A-Q-C such that segment PQ parallel side BC and segment PQ divides triangle ABC in two parts whose areas are equal .Find the value of BP/AB.

Answer 1

The value of BP/AB is 1.

Step-by-step explanation:

Given that segment PQ is parallel to side BC and divides triangle ABC into two equal parts, we can use the fact that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding side lengths. Let's denote the ratio of BP to AB as x. Since triangle AQP is similar to triangle ABC, the ratio of their corresponding side lengths is also x. Therefore, the ratio of the areas of triangle AQP to triangle ABC is x^2.

Since the areas of triangle AQP and triangle ABC are equal, we can set up the following equation:

x^2 = 1

Solving for x, we find that x = 1.

Therefore, BP/AB = 1.

Learn more about Triangle properties