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)

60.2 cm
116.3 cm
78.6 cm
92.9 cm

Answer 1

To find the length of the ramp that fits diagonally in the cage (which is shaped like a rectangular prism), we can use the 3D version of the Pythagorean theorem.

The formula to calculate the diagonal \(d\) of a rectangular prism is:

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

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 can substitute the values into the formula:

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

Calculating each term:

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

Now sum these values:

\[
4900 + 1225 + 2500 = 8625
\]

Now, take the square root:

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

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

The correct answer is \(92.9\) cm.