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)
• 60.2 ст
• 78.6 cm
• 116.3 cm
• 92.9 cm
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 representing the cage can be found by taking the square root of the sum of the squares of the length, width, and height.
Diagonal = √(70^2 + 35^2 + 50^2)
Diagonal = √(4900 + 1225 + 2500)
Diagonal = √(8625)
Diagonal ≈ 92.9 cm
Thus, the length of the ramp needs to be approximately 92.9 cm.
To find the length of the ramp needed to fit diagonally in the cage, we can use the Pythagorean Theorem. The diagonal of a rectangular prism can be found using the formula:
diagonal = √(length^2 + width^2 + height^2)
First, let's substitute the given values into the formula:
length = 70 cm
width = 35 cm
height = 50 cm
diagonal = √(70^2 + 35^2 + 50^2)
diagonal = √(4900 + 1225 + 2500)
diagonal = √(8625)
diagonal ≈ 92.9 cm
So, the length of the ramp needed to fit diagonally in the cage is approximately 92.9 cm. Therefore, the correct answer is:
• 92.9 cm
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-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the length of the cage (70 cm) will be one of the sides of the triangle, and the width (35 cm) and height (50 cm) will be the other two sides.
Let's calculate the length of the ramp:
Side A^2 + Side B^2 = Hypotenuse^2
35^2 + 50^2 = Hypotenuse^2
1225 + 2500 = Hypotenuse^2
3725 = Hypotenuse^2
To find the value of the hypotenuse, we need to take the square root of both sides:
Hypotenuse = √3725
Hypotenuse ≈ 61.0 cm
Therefore, the length of the ramp needed to fit diagonally in the cage is approximately 61.0 cm.
Since none of the provided answer options match exactly, we would round the answer to the nearest tenth:
The closest answer option is 60.2 cm.
here are the answers
1. 15.0
2. 59.5
3. 8.8
4. 9.1
5. 92.9
hope this helps! I just took this and got a 100