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.(
Responses

60.2 cm
60.2 cm

78.6 cm
78.6 cm

92.9 cm
92.9 cm

116.3 cm

Answer 1

To find the length of the ramp that fits diagonally in the cage (which is a rectangular prism), we can use the 3D diagonal formula:

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

where \( l \) is the length, \( w \) is the width, and \( h \) is the height of the rectangular prism.

Given:
- Length \( l = 70 \) cm
- Width \( w = 35 \) cm
- Height \( h = 50 \) cm

Now, we can plug 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 summing these values:

\[
4900 + 1225 + 2500 = 8625
\]

Now, we take the square root of 8625:

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

Thus, the length of the ramp needs to be approximately **92.9 cm**. Rounding is not necessary as it's already at one decimal place.

So, the correct answer is **92.9 cm**.