The triangles are similar by the AA Similarity Postulate. Find the value of x.
2 answers:
Answer: The required value of x is 7.5.
Step-by-step explanation: Given that the triangles shown in the figure are similar by AA similarity postulate.
We are to find the value of x.
We know that the corresponding sides of the similar triangles are proportional.
From the figure, we see that two pairs of corresponding sides in the triangles are (4.5, 3) and (x, 5).
Therefore, we must have
Thus, the required value of x is 7.5.
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Answer: Lattice parameter, a = (4R)/(√3)
Step-by-step explanation:
The typical arrangement of atoms in a unit cell of BCC is shown in the first attachment.
The second attachment shows how to obtain the value of the diagonal of the base of the unit cell.
If the diagonal of the base of the unit cell = x
(a^2) + (a^2) = (x^2)
x = a(√2)
Then, diagonal across the unit cell (a cube) makes a right angled triangle with one side of the unit cell & the diagonal on the base of the unit cell.
Let the diagonal across the cube be y
Pythagoras theorem,
(a^2) + ((a(√2))^2) = (y^2)
(a^2) + 2(a^2) = (y^2) = 3(a^2)
y = a√3
But the diagonal through the cube = 4R (evident from the image in the first attachment)
y = 4R = a√3
a = (4R)/(√3)
QED!!!
