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Home » Lavender Tree Shock: Could This Common Plant Actually Change Your Life? Find Out! - Baxtercollege

Lavender Tree Shock: Could This Common Plant Actually Change Your Life? Find Out! - Baxtercollege

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 \frac{y + z}{y - z} = 1 + \frac{2z}{y - z}, \quad \frac{z + x}{z - x} = \frac{z + x}{-(x - z)} = -\frac{z + x}{x - z} = -\left( \frac{(x - z) + 2z}{x - z} \right) = -1 - \frac{2z}{x - z}

📌 Adding the three:

📌 S = \left(1 + \frac{2y}{x - y}\right) + \left(1 + \frac{2z}{y - z}\right) + \left(-1 - \frac{2z}{x - z}\right)

📌 = 1 + \frac{2y}{x - y} + \frac{2z}{y - z} - \frac{2z}{x - z}

📌 S = 1 + 2\left( \frac{y}{x - y} + \frac{z}{y - z} - \frac{z}{x - z} \right)

📌 We now try a substitution to simplify. Let \( a = x - y > 0 \), \( b = y - z > 0 \), so \( x - z = a + b > 0 \). Then:

📌 x = z + b + a, \quad y = z + b

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h_c = \frac{2A}{c} = \frac{2 \times 84}{15} = \frac{168}{15} = 11.2
The shortest altitude is \( h_c \), so:
The hypotenuse of a right triangle is \( z \), and the radius of the i...
The area \( A \) of the right triangle with hypotenuse \( z \) and leg...
The radius \( r \) of the inscribed circle in a right triangle is give...
r = \frac{a + b - z}{2}
\text{Area of circle} = \pi r^2
The semi-perimeter \( s \) of the triangle is:
s = \frac{a + b + z}{2}
The area \( A \) can also be expressed as:

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