Asked by shhh
Use the pyramid and the given information to find the length of VM.
Given:
M is the midpoint of the pyramid's square base.
The square base ABCD has side lengths of 5 cm.
Lengths VA, VB, VC, and VD are each 8 cm.
A 5.3 cm
B 6.3 cm
C 7.2 cm
D 8.5 cm
Given:
M is the midpoint of the pyramid's square base.
The square base ABCD has side lengths of 5 cm.
Lengths VA, VB, VC, and VD are each 8 cm.
A 5.3 cm
B 6.3 cm
C 7.2 cm
D 8.5 cm
Answers
Answered by
GPT 3.5
To find the length of VM, we need to first find the height of the pyramid from point V to the base ABCD.
Since M is the midpoint of the square base ABCD, we can draw a line from V to M which is perpendicular to the base. This line will intersect the base at point K, forming a right triangle VKM.
Using the Pythagorean Theorem, we can find the height of the pyramid:
VM^2 = VK^2 + KM^2
Since VM = KM and VK = 5 cm/2 = 2.5 cm, we have:
VM^2 = (2.5 cm)^2 + (5 cm)^2
VM^2 = 6.25 cm^2 + 25 cm^2
VM^2 = 31.25 cm^2
VM = √31.25
VM ≈ 5.6 cm
Therefore, the length of VM is approximately 5.6 cm.
So, the correct answer is B. 6.3 cm
Since M is the midpoint of the square base ABCD, we can draw a line from V to M which is perpendicular to the base. This line will intersect the base at point K, forming a right triangle VKM.
Using the Pythagorean Theorem, we can find the height of the pyramid:
VM^2 = VK^2 + KM^2
Since VM = KM and VK = 5 cm/2 = 2.5 cm, we have:
VM^2 = (2.5 cm)^2 + (5 cm)^2
VM^2 = 6.25 cm^2 + 25 cm^2
VM^2 = 31.25 cm^2
VM = √31.25
VM ≈ 5.6 cm
Therefore, the length of VM is approximately 5.6 cm.
So, the correct answer is B. 6.3 cm