Question

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

78.6 cm
78.6 cm

60.2 cm
60.2 cm

116.3 cm
116.3 cm

92.9 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 distance formula. The formula for the diagonal \(d\) of a rectangular prism is given by:

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

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

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

Now, we will substitute the values into the formula:

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

Calculating each squared term:

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

Now, add these values together:

\[
4900 + 1225 + 2500 = 8625
\]

Now, find the square root of 8625:

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

Rounding to the nearest tenth results in:

\[
d \approx 92.9 \text{ cm}
\]

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