The length of the diagonal of a box is given by $D=\sqrt{L^{2}+W^{2}+H^{2}}$ where $L, W$, and $H$ are the length, width, and height of the box. Find the length of the diagonal, D, of a box that is $1 \mathrm{ft}$ long, $5 \mathrm{ft}$ high, and $4 \mathrm{ft}$ wide. Give the exact value.
A) $2 \sqrt{5} \mathrm{ft}$
B) $10 \mathrm{ft}$
C) $20 \mathrm{ft}$
D) $\sqrt{42} \mathrm{ft}$

Question

Quizplus · Accepted Answer

Substituting $L=1$, $W=4$, and $H=5$ into the formula $D=\sqrt{L^{2}+W^{2}+H^{2}}$ gives $D=\sqrt{1^2+4^2+5^2}=\sqrt{1+16+25}=\sqrt{42}$ ft.

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

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