Performing laplace transform of the equation.
sY(s) - y(0) + 6Y(s) = 1/(s-4)
(s+6)Y(s) - 2 = 1/(s-4)
Y(s) = 2/(s+6) + 1/(s-4)(s+6), by partial fraction decomposition
Y(s) = 2/(s+6) + 1/10 * (1/(s-4) + 1/(s+6))
Y(s) = 0.1/(s-4) + 2.1/(s+6)
Performing inverse laplace transform,
y(t) = 0.1e^4t + 2.1e^(-6t)
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The perimeter is 28".
The total length of three sides of the square = 28-5-5 = 18", so the side length of the square is 18/3 = 6".
The area of the triangle is ½(6)(4) = 12 square inches.
The area of the square is 6² = 36 square inches.
Total area = 12+36 = 48 square inches.
