To find the length of the ramp that fits diagonally in the cage (the diagonal of the rectangular prism), we can use the 3D distance formula. The formula for the diagonal \( d \) of a rectangular prism with length \( L \), width \( W \), and height \( H \) is:
\[ d = \sqrt{L^2 + W^2 + H^2} \]
Given:
- Length \( L = 70 \) cm
- Width \( W = 35 \) cm
- Height \( H = 50 \) cm
We can substitute these values into the formula:
\[ d = \sqrt{70^2 + 35^2 + 50^2} \]
Calculating each squared term:
\[ 70^2 = 4900 \] \[ 35^2 = 1225 \] \[ 50^2 = 2500 \]
Now, we can add these together:
\[ d = \sqrt{4900 + 1225 + 2500} \] \[ d = \sqrt{8625} \]
Now, we calculate the square root:
\[ d \approx 92.9 \text{ cm} \]
Thus, the length of the ramp that needs to fit diagonally in the cage is approximately 92.9 cm.
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