Question

In triangle abc ab=ac and ab:bc = 2:1 an perpendicular to bc then show that 4an squre = 15 bc square

Answer 1

Answer:

Step-by-step explanation:

Answer 2

4an² = 15bc² (Proved)

Step-by-step explanation:

See the diagram attached.

I is clear from the given conditions that Δ abc is an isosceles triangle with ab = ac = 2x (say) and bc = x (say).

Now, perpendicular on bc from a will bisect bc at n.

So, bn = cn = x/2.

Now, from the right triangle Δ anc, applying Pythagoras Theorem,

an² = ac² - cn² = $(2x)^{2} - (\frac{x}{2})^{2} = \frac{15x^{2}}{4}$

⇒ 4an² = 15bc² (Proved)