To find the length of the ramp that fits diagonally in the cage (which is shaped like a rectangular prism), we can use the 3D version of the Pythagorean theorem.
The formula to calculate the diagonal \(d\) of a rectangular prism is:
\[ d = \sqrt{l^2 + w^2 + h^2} \]
where \(l\) is the length, \(w\) is the width, and \(h\) is the height of the prism.
Given:
- Length \(l = 70\) cm
- Width \(w = 35\) cm
- Height \(h = 50\) cm
Now, we can substitute the values into the formula:
\[ d = \sqrt{(70)^2 + (35)^2 + (50)^2} \]
Calculating each term:
\[ 70^2 = 4900 \] \[ 35^2 = 1225 \] \[ 50^2 = 2500 \]
Now sum these values:
\[ 4900 + 1225 + 2500 = 8625 \]
Now, take the square root:
\[ d = \sqrt{8625} \approx 92.9 \text{ cm} \]
Thus, the length of the ramp needed to fit diagonally in the cage is approximately 92.9 cm.
The correct answer is \(92.9\) cm.
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