Math Problem Statement
Consider a triangle ABC such that B is a right angle. Let D and E be points on AC such that the triangle BDE is equilateral. If the area of triangle BDE is half of the area of triangle ABC, calculate the ratio of AC to DE.
Solution
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Math Problem Analysis
Mathematical Concepts
Geometry
Triangles
Area of Triangles
Equilateral Triangles
Ratios
Formulas
Area of a right triangle: (1/2) * base * height
Area of an equilateral triangle: (sqrt(3)/4) * side^2
Ratio: AC/DE = a/s
Theorems
Pythagorean Theorem
Properties of Equilateral Triangles
Suitable Grade Level
Grades 9-11