ABCD is a square. Equilateral triangles ACF and ABE are drawn on the the diagonal AC and side AB respectively. Find area of △ACF : area of △ABE. Plzz help me to do this
Answers
Given : ABCD is a square. Equilateral triangles ACF and ABE are drawn on the the diagonal AC and side AB respectively.
To find : area of △ACF : area of △ABE
Solution:
ABCD is a square
Let say AB = BC = CD = DA = x
AC² = AB² + BC² = x² + x² = 2x²
=>AC = x√2
ΔACF and Δ ABE are Equilateral triangles
Area of Δ ACF = (√3 / 4) AC²
Area of Δ ABE = (√3 / 4) AB²
Area of Δ ACF : Area of Δ ABE = (√3 / 4) AC² : (√3 / 4) AB²
=> Area of Δ ACF : Area of Δ ABE = AC² : AB²
=> Area of Δ ACF : Area of Δ ABE = 2x² : x²
=> Area of Δ ACF : Area of Δ ABE = 2 : 1
area of △ACF : area of △ABE = 2 : 1
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