To find the length of the ramp that fits diagonally in the cage (which is in the shape of a rectangular prism), we can use the formula for the space diagonal of a rectangular prism:
\[ d = \sqrt{l^2 + w^2 + h^2} \]
where:
- \(d\) is the diagonal length,
- \(l\) is the length,
- \(w\) is the width,
- \(h\) is the height.
In the case of Melissa's cage:
- \(l = 70 , \text{cm}\)
- \(w = 35 , \text{cm}\)
- \(h = 50 , \text{cm}\)
Substituting 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 sum these values:
\[ 4900 + 1225 + 2500 = 8625 \]
Now take the square root of the sum:
\[ d = \sqrt{8625} \]
Calculating the square root:
\[ d \approx 92.9 , \text{cm} \]
Rounding to the nearest tenth, the length of the ramp that Melissa needs is:
92.9 cm
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