`DeltaDEF` is an equilateral triangle. Seg `DPbot" side "EF,` and E-P-F. Prove that: `DP^(2)=3EP^(2)`

DeltaPQR is an equilateral triangle. Seg PS bot side QR such that Q-S-R . Prove PS^(2)=3QS^(2) by completing the following activity. In DeltaPQS , /_PSQ=square ……(Given) /_Q=square ………….(Angle of an equilateral triangle) :. /_QPS=30^(@) .................(Remaining angle of DeltaPQS ) :.DeltaPQS is a square triangle PS=square PQ .............(Side opposite to 60^(@) ).............. (1) and QS=square PQ ..........(Side opposite to 30^(@) ) PQ=2QS ..... (2) Substituting value of PQ from (2) in (1) PS=(sqrt(3))/(2)xx2QS :.PS=square QS :.PS^(2)=3QS^(2) ......(Square both the sides)

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

In the adjoining figure, DeltaPQR is an equilateral triangle. Point S is on seg QR. such that QS=(1)/(3)QR. Prove that : 9PS^(2)=7PQ^(2).

Prove that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Use the above theorem, in the following. If ABC is an equilateral triangle with AD bot BC , then prove that AD^(2) = 3DC^(2) .

What is the area of an equilateral triangle with side 2cm?

The area of an equilateral triangle with side 2sqrt3 cm is

In an equilateral triangle with side a, prove that area =(sqrt(3))/(4)a^(2)