The length of the diagonal of a box is given by $D=\sqrt{\mathrm{L}^{2}+\mathrm{W}^{2}+\mathrm{H}^{2}}$ where $\mathrm{L}, \mathrm{W}$, and $\mathrm{H}$ are the length, width, and height of the box. Find the length of the diagonal, D, of a box that is $2 \mathrm{ft}$ long, $2 \mathrm{ft}$ high, and $4 \mathrm{ft}$ wide. Give the exact value.
A) $8 \mathrm{ft}$
B) $2 \sqrt{6} \mathrm{ft}$
C) $16 \mathrm{ft}$
D) $4 \mathrm{ft}$

Question

Quizplus · Accepted Answer

The length of the diagonal is calculated using the formula $D=\sqrt{L^2+W^2+H^2}$. Substituting $L=2$, $W=4$, and $H=2$ into the formula gives $D=\sqrt{2^2+4^2+2^2}=\sqrt{4+16+4}=\sqrt{24}=2\sqrt{6}$ ft.

The Length of the Diagonal of a Box Is Given D=L2+W2+H2D=\sqrt{\mathrm{L}^{2}+\mathrm{W}^{2}+\mathrm{H}^{2}}D=L2+W2+H2​

The Length of the Diagonal of a Box Is Given $D=\sqrt{\mathrm{L}^{2}+\mathrm{W}^{2}+\mathrm{H}^{2}}$