To find the length of the ramp that fits diagonally in the cage, we need to calculate the space diagonal of the rectangular prism (the cage). The formula for the diagonal \(d\) of a rectangular prism with length \(l\), width \(w\), and height \(h\) is given by:
\[ d = \sqrt{l^2 + w^2 + h^2} \]
Using the dimensions provided:
- Length \(l = 70 \text{ cm}\)
- Width \(w = 35 \text{ cm}\)
- Height \(h = 50 \text{ cm}\)
Now we can substitute these values into the formula:
\[ d = \sqrt{(70)^2 + (35)^2 + (50)^2} \] \[ = \sqrt{4900 + 1225 + 2500} \] \[ = \sqrt{8625} \] \[ \approx 92.9 \text{ cm} \]
Therefore, the length of the ramp needs to be approximately 92.9 cm when rounded to the nearest tenth.
The correct response is:
92.9 cm
1 answer