Answer:
A(max) = 42.43 in²
Dimensions:
a = 7 in
b = 6,06 in
Step-by-step explanation: See annex
Equilateral triangle side L = 14 in, internal angles all equal to 60°
Let A area of rectangle A = a*b
side b tan∠60° = √3 tan∠60° = b/x b = √3 * x
side a a = L - 2x a = 14 - 2x
A(x) = a*b A(x) = ( 14 - 2x ) * √3 * x
A(x) = 14*√3*x - 2√3 * x²
Taking derivatives both sides of the equation
A´(x) = 14√3 - 4√3*x
A´(x) = 0 ⇒ 14√3 - 4√3*x = 0 ⇒ 14 - 4x = 0 x = 14/4
x = 3,5 in
Then
a = 14 - 2x a = 14 - 7 a = 7 in
b = √3*3,5 b = *√3 *3,5 b = 6,06 in
A(max) = 7 *6,06
A(max) = 42.43 in²
