Math Problem Statement

In a right-angled triangle ABC with ∠B = 90°, the length of side AB = 8 units and the length of side BC = 6 units. Point D is on side AC such that AD: DC=2:3. Point E is on side BC such that BE: EC = 3: 4. If the area of triangle BDE is maximized, what is the ratio of the areas of triangles BDE and ABC?

Your first skill is: Applying Geometric Concepts second skill Applying Propositional Logic

use these skills/topics to solve

Solution

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Math Problem Analysis

Mathematical Concepts

Geometry
Triangles
Area Ratios

Formulas

Pythagorean Theorem: AC = √(AB^2 + BC^2)
Area of Triangle: Area = (1/2) × base × height
Area Ratio based on Segment Division: Ratio = (AD/AC) × (BE/BC)

Theorems

Pythagorean Theorem
Area Proportions of Triangles

Suitable Grade Level

Grades 9-11