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Question
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.
Responses
A 5.3 cm5.3 cm
B 6.3 cm6.3 cm
C 7.2 cm7.2 cm
D 8.5 cm
To find the length of VM, we can use the Pythagorean theorem. Since M is the midpoint of the base, we can split the square base into two right triangles, with one leg being VM. The hypotenuse of each right triangle is the diagonal of the square base, which can be found using the Pythagorean theorem:
Diagonal = √(5^2 + 5^2)
Diagonal = √50
Diagonal = 5√2
Now, we can find VM using the Pythagorean theorem in one of the right triangles:
VM = √(8^2 - (5√2)^2)
VM = √(64 - 50)
VM = √14
Therefore, the length of VM is approximately 3.7 cm. None of the given response choices match this calculation, so there may be a mistake in the question or the choices provided.