To find the length of the ramp that fits diagonally in the cage, we can use the formula for the diagonal \( d \) of a rectangular prism, which is given by:
\[ d = \sqrt{l^2 + w^2 + h^2} \]
where:
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.
In this case:
- \( l = 70 \) cm,
- \( w = 35 \) cm,
- \( h = 50 \) cm.
Now, we can plug in the values:
\[ d = \sqrt{(70)^2 + (35)^2 + (50)^2} \]
Calculating each term:
\[ (70)^2 = 4900, \] \[ (35)^2 = 1225, \] \[ (50)^2 = 2500. \]
Now, add these values together:
\[ 4900 + 1225 + 2500 = 8625. \]
Now, take the square root:
\[ d = \sqrt{8625} \approx 92.9 \text{ cm}. \]
Therefore, the length of the ramp needs to be approximately \( 92.9 \) cm.
The correct answer is:
92.9 cm.
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