Question
Mellisa has a gerbil that lives in a cage in the shape of a rectangular pro she wants to put a ramp in the cage to give her gerbil exercise the cage has a length of 70 width 35 and height 50 how lo g the ramp need to be to fit diagonally in the cage
Answers
Answered by
GPT-4o mini
To find the length of the ramp that will fit diagonally in the rectangular cage, we can use the 3-dimensional distance formula. The diagonal \( d \) of a rectangular prism can be calculated using the 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 cage.
Given:
- Length \( l = 70 \) (units)
- Width \( w = 35 \) (units)
- Height \( h = 50 \) (units)
Substituting these values into the formula:
\[
d = \sqrt{70^2 + 35^2 + 50^2}
\]
Calculating the squares:
\[
70^2 = 4900
\]
\[
35^2 = 1225
\]
\[
50^2 = 2500
\]
Now, summing these values:
\[
d = \sqrt{4900 + 1225 + 2500} = \sqrt{8625}
\]
Now calculating \( \sqrt{8625} \):
\[
\sqrt{8625} \approx 92.9
\]
Thus, the length of the ramp should be approximately **92.9 units** to fit diagonally in the cage.
\[
d = \sqrt{l^2 + w^2 + h^2}
\]
where \( l \) is the length, \( w \) is the width, and \( h \) is the height of the cage.
Given:
- Length \( l = 70 \) (units)
- Width \( w = 35 \) (units)
- Height \( h = 50 \) (units)
Substituting these values into the formula:
\[
d = \sqrt{70^2 + 35^2 + 50^2}
\]
Calculating the squares:
\[
70^2 = 4900
\]
\[
35^2 = 1225
\]
\[
50^2 = 2500
\]
Now, summing these values:
\[
d = \sqrt{4900 + 1225 + 2500} = \sqrt{8625}
\]
Now calculating \( \sqrt{8625} \):
\[
\sqrt{8625} \approx 92.9
\]
Thus, the length of the ramp should be approximately **92.9 units** to fit diagonally in the cage.
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