To find the length of the ramp that fits diagonally in a rectangular prism-shaped cage, we can use the three-dimensional version of the Pythagorean Theorem. For a rectangular prism (box), the formula for the diagonal \( d \) 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, the dimensions of Melissa's gerbil cage are given as:
- Length \( l = 70 \) cm
- Width \( w = 35 \) cm
- Height \( h = 50 \) cm
Substituting these values into the formula, we calculate:
\[ d = \sqrt{70^2 + 35^2 + 50^2} \]
Calculating each component:
\[ 70^2 = 4900 \quad (1) \] \[ 35^2 = 1225 \quad (2) \] \[ 50^2 = 2500 \quad (3) \]
Now add these results together:
\[ 4900 + 1225 + 2500 = 8625 \]
Now take the square root of the total:
\[ d = \sqrt{8625} \approx 92.9 \text{ cm} \]
Rounding to the nearest tenth:
\[ d \approx 92.9 \text{ cm} \]
Thus, the correct response is:
92.9 cm
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