Melissa has a gerbil that lives in a cage in the shape of a rectangular prism. She wants to put a

Question

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)
78.6 cm
60.2 cm
92.9 cm
116.3 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 of the prism.

Given:

• Length \( l = 70 \) cm
• Width \( w = 35 \) cm
• Height \( h = 50 \) cm

We can substitute these values into the formula:

\[ d = \sqrt{(70)^2 + (35)^2 + (50)^2} \] \[ d = \sqrt{4900 + 1225 + 2500} \] \[ d = \sqrt{8625} \]

Now we calculate the square root:

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

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

The answer is 92.9 cm.