To find the length of the ramp that fits diagonally in the cage (which is a rectangular prism), we can use the 3D diagonal 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 rectangular prism.
Given:
- Length \( l = 70 \) cm
- Width \( w = 35 \) cm
- Height \( h = 50 \) cm
Now, we can plug these values into the formula:
\[ d = \sqrt{70^2 + 35^2 + 50^2} \]
Calculating each square:
\[ 70^2 = 4900 \] \[ 35^2 = 1225 \] \[ 50^2 = 2500 \]
Now summing these values:
\[ 4900 + 1225 + 2500 = 8625 \]
Now, we take the square root of 8625:
\[ d = \sqrt{8625} \approx 92.9 , \text{cm} \]
Thus, the length of the ramp needs to be approximately 92.9 cm. Rounding is not necessary as it's already at one decimal place.
So, the correct answer is 92.9 cm.