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 92.9 cm 92.9 cm 78.6 cm 78.6 cm 116.3 cm 116.3 cm 60.2 cm

Answer 1

To find the length of the ramp that fits diagonally inside the rectangular prism (the cage), we can use the 3D diagonal formula. The formula for the diagonal \( d \) of a rectangular prism with length \( l \), width \( w \), and height \( h \) is:

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

Given the dimensions of the cage:

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

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, adding these values together:

\[ d = \sqrt{4900 + 1225 + 2500} = \sqrt{8625} \]

Now, we calculate \( \sqrt{8625} \):

\[ \sqrt{8625} \approx 93 \]

When rounded to the nearest tenth, we find that the length of the ramp is approximately:

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

Thus, the answer is 92.9 cm.