Question

In a equilateral triangle ABC , D is a point on side BC such that BD = 1/4 BC . Prove that 16 AD² = 13 BC².​

Answer 1

Given:- D is a point on the side BC of the equilateral triangle such that BD=1/4BC.

To Prove:- 16AD² = 13BC²

Construction:- Draw AE perpendicular to BC

Proof:-★ In ∆AED we have,

→AD²=AE²+DE²...........( by Pythagoras theorem)-(1)

★In ∆AEB we have,

→AB²=AE²+BE²..…...(by Pythagoras theorem)-(2)

Now,

Putting the value of AE² from the equation (1)&(2) we get,

→AD²=AB²-BE²+DE²

→AD²=BC² - (BC/2)² + (BE - BD)²

→BC²- BC²/4 + {BC/2 - BC/4}²

→BC² - BC²/4 + BC²/16

→(16BC² - 4 BC² + BC²)= 13BC²/16

Now, AD²= 13 BC²/16

Taking 16 to the left we get,

16AD²= 13 BC².

Hence proved!!

Answer 2

Original cost of machinery = Rs 14,80,000

Installation charges = Rs. 1,20,000

Estimated useful life of Asset in years = 5

Scrap value = Rs. 80,000

Find :

I). The amount of annual Deprec