If an equilateral triangle ABCD is a point on the side BC such that BD = `1/3`, prove that `9 AD^2 = 7AB^2`.

The perimeters of two similar triangles are 25cm and 15cm respectively. If one side of the first triangle is 9cm, find the length of the corresponding side of the second triangle. OR In an equilateral triangle ABC, D is a point on side BC such that BD = 1/3 BC. Prove that 9 AD^(2)=7AB^(2)

In an equilateral triangle ABC,D is a point on side BC such that BD=(1)/(3)BC Prove that 9AD^(2)=7AB^(2)

DeltaABC is an equilateral triangle. Point D is on side BC such that BD=(1)/(5)BC then prove 25AD^(2)=21AB^(2) .

In an equilateral triangleABC, AD is the altitude drawn from A on the side BC. Prove that 3AB^(2) = 4AD^(2)

In an equilateral triangle ABC the side BC is trisected at D. Prove that 9AD^(2)=7AB^(2)

The side AB of an equilateral triangle ABC is produced to D such that BD=2AC the value of (CD^(2))/(AB^(2))is

If E is a point on side r:A of an equilateral triangle ABC such that BE bot CA , then prove that AB^(2) +BC^(2) +CA^(2) = 4BE^(2) .

ABC is an isosceles triangle with AB=AC and D is a pooint on AC such that BC^(2)=ACxCD .Prove that BD=BC

In DeltaABC, D is any point on side BC. Prove that AB+BC+CA gt 2AD