Question

Find the length of the diagonal of 7cm x 6 cm x 12 cm rectangular prism. Round to the nearest tenth.

Answer 1

15.1 cm

Explantion

Step 1

to solve this we can use the distance between 2 points formula, it is

$\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2} \\ \text{where} \\ P1(x_1,y_1,z_1) \\ P2(x_2,y_2,z_2) \end{gathered}$

Step 1

Let

$\begin{gathered} P1(0,0,0) \\ P2(7,6,12) \end{gathered}$

now, replace in the formula

$\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2} \\ d=\sqrt[]{(7-0)^2+(6-0)^2+(12-0)^2} \\ d=\sqrt[]{7^2+6^2+12^2} \\ d=\sqrt[]{7^2+6^2+12^2} \\ d=\sqrt[]{229} \\ d=15.13 \\ \text{rounded } \\ d=15.1 \end{gathered}$

therefore, the answer is

15.1 cm

I hope this helps you