To find the length of the ramp that fits diagonally in the cage (which is a rectangular prism), we can use the three-dimensional distance formula. The formula for the diagonal, \(d\), of a rectangular prism with dimensions length \(l\), width \(w\), and height \(h\) is given by:
\[ d = \sqrt{l^2 + w^2 + h^2} \]
In this case, the dimensions of the cage are:
- Length \(l = 70 , \text{cm}\)
- Width \(w = 35 , \text{cm}\)
- Height \(h = 50 , \text{cm}\)
Now we can plug in these values into the formula:
\[ d = \sqrt{(70)^2 + (35)^2 + (50)^2} \]
First, calculate each term:
\[ (70)^2 = 4900 \] \[ (35)^2 = 1225 \] \[ (50)^2 = 2500 \]
Now, add these together:
\[ 4900 + 1225 + 2500 = 8625 \]
Next, take the square root:
\[ d = \sqrt{8625} \approx 92.9 , \text{cm} \]
Thus, the length of the ramp that fits diagonally in the cage is approximately \(92.9 , \text{cm}\).
Therefore, the correct answer is:
1. 92.9 cm
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