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) Responses 60.2 cm 60.2 cm 78.6 cm 78.6 cm 116.3 cm 116.3 cm 92.9 cm 92.9 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:

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

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

In this case:
- \(l = 70\) cm,
- \(w = 35\) cm,
- \(h = 50\) cm.

Now, let's calculate the diagonal.

First, we square each dimension:

\[
l^2 = 70^2 = 4900
\]
\[
w^2 = 35^2 = 1225
\]
\[
h^2 = 50^2 = 2500
\]

Now, we add these values together:

\[
l^2 + w^2 + h^2 = 4900 + 1225 + 2500 = 8625
\]

Next, we take the square root of the total:

\[
d = \sqrt{8625} \approx 92.9 \text{ cm}
\]

Therefore, the length of the ramp needed to fit diagonally in the cage is approximately **92.9 cm**.