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 a 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 around your answer to the nearest tenth
To find the length of the ramp needed to fit diagonally in the cage, we can use the Pythagorean theorem.
The diagonal of the rectangular prism can be found by applying the Pythagorean theorem to the three dimensions of the cage.
Let's label the dimensions as follows:
Length = 70 cm
Width = 35 cm
Height = 50 cm
Using the Pythagorean theorem, we have:
Diagonal^2 = Length^2 + Width^2 + Height^2
Substituting the given values, we get:
Diagonal^2 = 70^2 + 35^2 + 50^2
Diagonal^2 = 4900 + 1225 + 2500
Diagonal^2 = 8625
Taking the square root of both sides, we have:
Diagonal ≈ √8625 ≈ 92.9 cm
So, the ramp needs to be approximately 92.9 cm long to fit diagonally in the cage.
To find the length of the ramp needed to fit diagonally in the cage, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the length, width, and height of the rectangular prism form a right triangle. The length and width of the cage make up the base and height of the triangle, and the ramp will be the hypotenuse.
Using the Pythagorean theorem,
Length of the ramp = √(Length of cage^2 + Width of cage^2 + Height of cage^2)
Plugging in the values,
Length of the ramp = √(70^2 + 35^2 + 50^2)
Length of the ramp = √(4900 + 1225 + 2500)
Length of the ramp = √(8625)
Length of the ramp ≈ 92.8 cm
Therefore, the ramp needs to be approximately 92.8 cm long to fit diagonally in the cage.
To find the length of the ramp needed to fit diagonally in the cage, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the length, width, and height of the cage form a right triangle. The length of the ramp will be the hypotenuse of this triangle.
Let's label the length of the ramp as 'r'. According to the Pythagorean theorem, we have the equation:
r^2 = length^2 + width^2 + height^2
Substituting the given values:
r^2 = 70^2 + 35^2 + 50^2
Simplifying:
r^2 = 4900 + 1225 + 2500
r^2 = 8625
To find the length of the ramp, we need to take the square root of both sides:
r ≈ √8625
Using a calculator, we find that the square root of 8625 is approximately 92.8.
Therefore, the length of the ramp needed to fit diagonally in the cage is approximately 92.8 cm (rounded to the nearest tenth).