w' = w - c,\quad h' = h - c,\quad p \le w' \ \text{且}\ q \le h'

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <msup><mi>w</mi><mo>′</mo></msup><mo>=</mo><mi>w</mi><mo>−</mo><mi>c</mi>
    <mo>,</mo>
    <msup><mi>h</mi><mo>′</mo></msup><mo>=</mo><mi>h</mi><mo>−</mo><mi>c</mi>
    <mo>,</mo>
    <mi>p</mi><mo>≤</mo><msup><mi>w</mi><mo>′</mo></msup>
    <mo>∧</mo>
    <mi>q</mi><mo>≤</mo><msup><mi>h</mi><mo>′</mo></msup>
  </mrow>
</math>

w' = w - c,  h' = h - c,  p <= w' and q <= h'

weff = w - c; heff = h - c; fits = (p <= weff && q <= heff) || (q <= weff && p <= heff)

weff := w - c;  heff := h - c;  fits := (p <= weff and q <= heff) or (q <= weff and p <= heff);

weff = w - c; heff = h - c; fits = (p <= weff && q <= heff) || (q <= weff && p <= heff);  % p, q 是朝向開口的面的兩邊

w' = w − c, h' = h − c, p ≤ w' ∧ q ≤ h'

W_{\theta} = p\cos\theta + q\sin\theta,\quad H_{\theta} = p\sin\theta + q\cos\theta,\quad W_{\theta} \le w' \ \text{且}\ H_{\theta} \le h'

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <msub><mi>W</mi><mi>θ</mi></msub><mo>=</mo>
    <mi>p</mi><mo>&#x2062;</mo><mi>cos</mi><mo>&#x2061;</mo><mi>θ</mi>
    <mo>+</mo>
    <mi>q</mi><mo>&#x2062;</mo><mi>sin</mi><mo>&#x2061;</mo><mi>θ</mi>
    <mo>,</mo>
    <msub><mi>H</mi><mi>θ</mi></msub><mo>=</mo>
    <mi>p</mi><mo>&#x2062;</mo><mi>sin</mi><mo>&#x2061;</mo><mi>θ</mi>
    <mo>+</mo>
    <mi>q</mi><mo>&#x2062;</mo><mi>cos</mi><mo>&#x2061;</mo><mi>θ</mi>
  </mrow>
</math>

W_theta = p cos theta + q sin theta,  H_theta = p sin theta + q cos theta

{p*Cos[theta] + q*Sin[theta], p*Sin[theta] + q*Cos[theta]}  (* theta 是弧度，用度時寫 theta Degree *)

Wt := p*cos(theta) + q*sin(theta);  Ht := p*sin(theta) + q*cos(theta);

Wt = p*cosd(theta) + q*sind(theta); Ht = p*sind(theta) + q*cosd(theta);  % theta 的單位是度

W_θ = p cos θ + q sin θ, H_θ = p sin θ + q cos θ

L_{\max} = \left(a^{2/3} + b^{2/3}\right)^{3/2},\quad L(\theta) = \frac{a}{\sin\theta} + \frac{b}{\cos\theta} - \frac{d}{\sin\theta\cos\theta},\quad L_{\max} = \min_{0 < \theta < 90^\circ} L(\theta)

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <msub><mi>L</mi><mi>max</mi></msub><mo>=</mo>
    <msup>
      <mrow><mo>(</mo><msup><mi>a</mi><mrow><mn>2</mn><mo>/</mo><mn>3</mn></mrow></msup><mo>+</mo><msup><mi>b</mi><mrow><mn>2</mn><mo>/</mo><mn>3</mn></mrow></msup><mo>)</mo></mrow>
      <mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow>
    </msup>
    <mo>,</mo>
    <mi>L</mi><mo>(</mo><mi>θ</mi><mo>)</mo><mo>=</mo>
    <mfrac><mi>a</mi><mrow><mi>sin</mi><mo>&#x2061;</mo><mi>θ</mi></mrow></mfrac>
    <mo>+</mo>
    <mfrac><mi>b</mi><mrow><mi>cos</mi><mo>&#x2061;</mo><mi>θ</mi></mrow></mfrac>
    <mo>−</mo>
    <mfrac><mi>d</mi><mrow><mi>sin</mi><mo>&#x2061;</mo><mi>θ</mi><mo>&#x2062;</mo><mi>cos</mi><mo>&#x2061;</mo><mi>θ</mi></mrow></mfrac>
  </mrow>
</math>

L_max = (a^(2/3) + b^(2/3))^(3/2),  L(theta) = a/sin theta + b/cos theta - d/(sin theta cos theta)

lrod = (a^(2/3) + b^(2/3))^(3/2); NMinimize[{a/Sin[t] + b/Cos[t] - d/(Sin[t]*Cos[t]), 0.01 < t < Pi/2 - 0.01}, t]

lrod := (a^(2/3) + b^(2/3))^(3/2);  L := theta -> a/sin(theta) + b/cos(theta) - d/(sin(theta)*cos(theta));  Lmax := minimize(L(theta), theta = 0.01 .. Pi/2 - 0.01);

lrod = (a^(2/3) + b^(2/3))^(3/2); L = @(t) a./sin(t) + b./cos(t) - d./(sin(t).*cos(t)); [t0, Lmax] = fminbnd(L, 0.01, pi/2 - 0.01);  % t 是弧度

L_max = (a^(2/3) + b^(2/3))^(3/2), L(θ) = a/sin θ + b/cos θ − d/(sin θ cos θ)

D_{\text{底面}} = \sqrt{a^{2}+b^{2}},\quad D_{\text{側面}} = \sqrt{b^{2}+h^{2}},\quad D_{\text{空間}} = \sqrt{a^{2}+b^{2}+h^{2}}

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <msub><mi>D</mi><mtext>底面</mtext></msub><mo>=</mo>
    <msqrt><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup></msqrt>
    <mo>,</mo>
    <msub><mi>D</mi><mtext>側面</mtext></msub><mo>=</mo>
    <msqrt><msup><mi>b</mi><mn>2</mn></msup><mo>+</mo><msup><mi>h</mi><mn>2</mn></msup></msqrt>
    <mo>,</mo>
    <msub><mi>D</mi><mtext>空間</mtext></msub><mo>=</mo>
    <msqrt><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup><mo>+</mo><msup><mi>h</mi><mn>2</mn></msup></msqrt>
  </mrow>
</math>

D_floor = sqrt(a^2 + b^2),  D_side = sqrt(b^2 + h^2),  D_space = sqrt(a^2 + b^2 + h^2)

{Sqrt[a^2 + b^2], Sqrt[b^2 + h^2], Sqrt[a^2 + b^2 + h^2]}

Dfloor := sqrt(a^2 + b^2);  Dside := sqrt(b^2 + h^2);  Dspace := sqrt(a^2 + b^2 + h^2);

Dfloor = sqrt(a^2 + b^2); Dside = sqrt(b^2 + h^2); Dspace = sqrt(a^2 + b^2 + h^2);  % a, b, h 是車廂的有效內部尺寸

D_底面 = √(a^2 + b^2), D_側面 = √(b^2 + h^2), D_空間 = √(a^2 + b^2 + h^2)