The area of an equilateral triangle is 6√3 times the area of a rhombus whose one side measures 13 cm and one diagonal is 10 cm. The length of side of the triangle, in cm, is:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 24√5
Area of Rhombus = Diagonal1 × Diagonal2/2
Diagonals of Rhombus bisects each other at 90 degree
By using pythagoras theorem we get,
Diagonal2/2 = √(132 - 52), Diagonal2/2 = √144 = 12
Diagonal2 = 24
Area of Rhombus = 10 × 24/2 = 120 cm2
Area of equilateral triangle = √3 × side2/4
The area of an equilateral triangle is 6√3 times the area of a rhombus i.e,
6√3 × 120 = 720√3, 720√3 = √3 × side2/4
2160 = side2 , side = 24√5