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:
\[ d = \sqrt{l^2 + w^2 + h^2} \]
where \(l\) is the length, \(w\) is the width, and \(h\) is the height of the prism.
Given the dimensions of the cage:
- Length \(l = 70\) cm
- Width \(w = 35\) cm
- Height \(h = 50\) cm
Now, we will substitute 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, we add these squares together:
\[ 4900 + 1225 + 2500 = 8625 \]
Next, we take the square root of 8625:
\[ d = \sqrt{8625} \approx 92.9 \]
Rounding to the nearest tenth, the length of the ramp that fits diagonally in the cage is:
\[ \boxed{92.9 \text{ cm}} \]