Prove that three times the square of any side of an equilateral-triangle is equal to four times the square of the altitude.

Prove that three times the sum of the squares of the sides of a triangle is equal to four times the sum of the squares of the medians of the triangle.

In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes.

In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes.

Prove that the medians of an equilateral triangle are equal.

Prove that the medians of an equilateral triangle are equal.

Prove that the area of an equilateral triangle is equal to (sqrt(3))/4a^2, where a is the side of the triangle.

If side(a)=4 then area of the equilateral triangle DeltaABC is equal to

Fill in the balnks : (i) In a right triangle, the square of the hypotenuse is equal to the……….of the square of the other two sides. (ii) If the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is......... (iii) Of all the line segments that can be drawn to a given line form a given point outside it, the.............is the shortest.

The side of an equilatetral triangle has the same length as the diagonal of a square. What is the area of the square? (1) The height of the equilateral triangle is equal to 6sqrt(3) . (2) The area of the equilateral triangle is equal to 36sqrt(3) .

Prove that the sum of the squares of the diagonals of parallelogram is equal to the sum of the squares of its sides.