A circus tent is in the shape of a square pyramid. Each edge of the square base is 20 m and its slant height is 13.5 m. Find the height of the tent. Round the answer to the nearest tenth.(1 point)
Responses
16.8 m
16.8 m
14.8 cm
14.8 cm
24.1 cm
24.1 cm
9.1 m
First, let's find the height of the tent using the Pythagorean theorem.
The slant height represents the hypotenuse of a right triangle formed by the height of the tent, the slant height, and half of the length of the base.
Let's call the height of the tent h. Using the Pythagorean theorem, we can write:
h^2 + (10)^2 = (13.5)^2
Simplifying:
h^2 + 100 = 182.25
Subtracting 100 from both sides:
h^2 = 82.25
Taking the square root of both sides:
h ≈ 9.1 m
Therefore, the height of the tent is approximately 9.1 m.
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
60.2 cm
60.2 cm
92.9 cm
92.9 cm
116.3 cm
116.3 cm
78.6 cm
To find the length of the ramp, we need to find the diagonal of the rectangular prism. We can use the Pythagorean theorem to do this.
The diagonal represents the hypotenuse of a right triangle formed by the length, width, and height of the prism.
Let's call the length of the ramp d. Using the Pythagorean theorem, we can write:
d^2 = (70)^2 + (35)^2 + (50)^2
Simplifying, we get:
d^2 = 4900 + 1225 + 2500
d^2 = 8625
Taking the square root of both sides, we get:
d ≈ 92.9 cm
Therefore, the length of the ramp needs to be approximately 92.9 cm.