Math Problem Statement
The area of an equilateral triangle is A = (s^2√3/ 4 where, s denotes the length of each side. Suppose, the length s of each side of an equilateral triangle is increasing at a rate of √7 feet per hour. 3 Find the rate of change of its area A when s = 8 feet.
Solution
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Math Problem Analysis
Mathematical Concepts
Differentiation
Implicit Differentiation
Geometry of Triangles
Formulas
Area of an equilateral triangle: A = (s^2√3) / 4
Implicit differentiation: dA/dt = (√3/2) * s * ds/dt
Theorems
Differentiation rules
Chain rule in calculus
Suitable Grade Level
Grades 11-12 (Calculus)
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