Question

Melissa has a gerbil that lives in a cage in the shape of a rectangular prism. She wants to put a ramp in the cage to give her gerbil exercise. The cage has a length of 70 cm, a width of 35 cm, and a height of 50 cm. How long does the ramp need to be to fit diagonally in the cage? Round the answer to the nearest tenth.(1 point)Responses78.6 cm 78.6 cm 116.3 cm116.3 cm92.9 cm92.9 cm60.2 cm

Answer 1

To find the length of the ramp that fits diagonally in the cage, we can use the formula for the diagonal \(d\) of a rectangular prism, which is given by:

\[
d = \sqrt{l^2 + w^2 + h^2}
\]

where:
- \(l\) is the length,
- \(w\) is the width,
- \(h\) is the height.

Given:
- \(l = 70 \, \text{cm}\),
- \(w = 35 \, \text{cm}\),
- \(h = 50 \, \text{cm}\).

Now we plug in the values:

\[
d = \sqrt{70^2 + 35^2 + 50^2}
\]

Calculating each term:

\[
70^2 = 4900,
\]
\[
35^2 = 1225,
\]
\[
50^2 = 2500.
\]

Adding these together:

\[
4900 + 1225 + 2500 = 8625.
\]

Now, we take the square root:

\[
d = \sqrt{8625} \approx 93.0 \, \text{cm}.
\]

Rounding to the nearest tenth gives us \(92.9 \, \text{cm}\).

Thus, the length of the ramp needs to be approximately **92.9 cm**.