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

1 answer

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.