Question

need step by step explanation..
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Answer 1

Answer:

Step-by-step explanation:

➡️ABC is a triangle right angled at B, and D and E are points of trisection of BC.

➡️Let BD = DE = EC = x

➡️Then BE = 2x and BC = 3x

➡️In Δ ABD,

AD² = AB² + BD²

AD² = AB² + x²

➡️In Δ ABE,

AE² = AB² + BE²

AE² = AB² + (2x)²

AE² = AB² + 4x²

➡️In Δ ABC,

AC² = AB² + BC²  

AC² = AB + (3x)²

AC² = AB² + 9x²

➡️3AC² + 5AD² = 3(AB² + 9x²) + 5(AB² + x²) 

8AB² + 32x²

8(AB² + 4x²)

➡️8AE²

➡️ 8AE² = 3AC² + 5AD²

Hence proved.

Hope it helps..

Answer 2

Answer:

We know that when A is extended to points D and E respectively it trisects the line BC

Step-by-step explanation:

so first take triangl ABD and ABC and write equation in form of Pythagoras theorem and multiply them with 3 And 5 respectively and then write BC as 1/3 bc=bd respectively your answer will come