To find the length of the diagonal of a rectangular prism, you can use the formula:
\[ d = \sqrt{l^2 + w^2 + h^2} \]
where \( l \) is the length, \( w \) is the width, and \( h \) is the height of the prism.
In this case, the dimensions of the prism are:
- Length (\( l \)) = 24 cm
- Width (\( w \)) = 6 cm
- Height (\( h \)) = 8 cm
Now, we can plug these values into the formula:
\[ d = \sqrt{(24)^2 + (6)^2 + (8)^2} \]
Calculating each part:
\[ (24)^2 = 576 \] \[ (6)^2 = 36 \] \[ (8)^2 = 64 \]
Now sum these values:
\[ d = \sqrt{576 + 36 + 64} \] \[ d = \sqrt{676} \]
Finally, calculate the square root:
\[ d = 26 \text{ cm} \]
So, the length of the diagonal of the prism is 26 cm.
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