In an equilateral `triangleABC, AD` is the altitude drawn from A on the side BC. Prove that `3AB^(2) = 4AD^(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 (Fig. 6.2), AD is an altitude. Then 4AD^2 is equal to

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

In equilateral triangleABC, ADbotBC. Prove that 3BC^2= 4AD^2.

AD is an altitude of an equilateral triangle ABC .On AD as base,another equiliateral triangle ADE is constructed.Prove that Area (ADE): Area (ABC)=3:4.

The following figure shows a triangle ABC in which AD is a median and AE bot BC . Prove that 2AB^(2)+ 2AC^(2) = 4AD^(2) + BC^(2) .

In an equilateral triangle with side a, prove that the altitude is of length (asqrt3)/2

In a right triangle ABC, right angled at A, AD is drawn perpendicular to BC. Prove that: AB^(2)-BD^(2)= AC^(2)-CD^(2)

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