Question

find the length of the diagonal d of the rectangular box shown in the figure. d =

Explanation:

Step1: Recall the 3D diagonal formula

For a rectangular box with length \( l \), width \( w \), height \( h \), the diagonal \( d \) is given by \( d=\sqrt{l^{2}+w^{2}+h^{2}} \). Here, \( l = 12 \), \( w = 4 \), \( h = 3 \).

Step2: Substitute values into the formula

Substitute \( l = 12 \), \( w = 4 \), \( h = 3 \) into the formula: \( d=\sqrt{12^{2}+4^{2}+3^{2}} \).

Step3: Calculate the squares

Calculate \( 12^{2}=144 \), \( 4^{2}=16 \), \( 3^{2}=9 \). Then sum them: \( 144 + 16+9=169 \).

Step4: Take the square root

Take the square root of 169: \( \sqrt{169}=13 \).

Answer:

\( 13 \)