To find the length of the ramp needed to fit diagonally in the cage, we can use the 3-dimensional version of the Pythagorean theorem. The formula to find 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.
In this case, Melissa's cage has the following dimensions:
- Length \( l = 70 \) cm
- Width \( w = 35 \) cm
- Height \( h = 50 \) cm
Now, we will calculate the diagonal:
\[ D = \sqrt{(70)^2 + (35)^2 + (50)^2} \]
Calculating each of the squares:
\[ (70)^2 = 4900 \] \[ (35)^2 = 1225 \] \[ (50)^2 = 2500 \]
Now, summing these values:
\[ D = \sqrt{4900 + 1225 + 2500} = \sqrt{8625} \]
Now, we calculate \( \sqrt{8625} \):
\[ D \approx 92.9 \text{ cm} \]
Rounding to the nearest tenth, the length of the ramp needed to fit diagonally in the cage is approximately 92.9 cm. Therefore, the correct answer is:
92.9 cm
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