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.
Given:
- \(l = 70 , \text{cm}\),
- \(w = 35 , \text{cm}\),
- \(h = 50 , \text{cm}\).
Now we plug in the values:
\[ d = \sqrt{70^2 + 35^2 + 50^2} \]
Calculating each term:
\[ 70^2 = 4900, \] \[ 35^2 = 1225, \] \[ 50^2 = 2500. \]
Adding these together:
\[ 4900 + 1225 + 2500 = 8625. \]
Now, we take the square root:
\[ d = \sqrt{8625} \approx 93.0 , \text{cm}. \]
Rounding to the nearest tenth gives us \(92.9 , \text{cm}\).
Thus, the length of the ramp needs to be approximately 92.9 cm.
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