Solve the problem.
-A formula for the length of a diagonal from the upper corner of a box to the opposite lower corner is $\mathrm { d } = \sqrt { \mathrm { L } ^ { 2 } + \mathrm { W } ^ { 2 } + \mathrm { H } ^ { 2 } }$, where $\mathrm { L } , \mathrm { W }$, and H are the length, width, and height, respectively. Find the length of the diagonal of the box if the length is 23 inches, width is 15 inches, and height is 8 inches. Leave your answer in simplified radical form.
A) $\sqrt { 818 }$ in.
B) $2 \sqrt { 23 } \mathrm { in }$.
C) $\sqrt { 46 } \mathrm { in }$.
D) $2 \sqrt { 409 } \mathrm { in }$.

Question

Quizplus · Accepted Answer

The formula for the diagonal is $d = \sqrt{L^2 + W^2 + H^2}$. Substituting $L = 23$, $W = 15$, and $H = 8$, we get $d = \sqrt{23^2 + 15^2 + 8^2} = \sqrt{529 + 225 + 64} = \sqrt{818}$ inches.

Solve the Problem d=L2+W2+H2\mathrm { d } = \sqrt { \mathrm { L } ^ { 2 } + \mathrm { W } ^ { 2 } + \mathrm { H } ^ { 2 } }d=L2+W2+H2​

Solve the Problem $\mathrm { d } = \sqrt { \mathrm { L } ^ { 2 } + \mathrm { W } ^ { 2 } + \mathrm { H } ^ { 2 } }$