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The length of a diagonal of a cube with concutive vertices (3,9) and (3,7) is a. 2 units b. 4 units c. 2√2 units d. 2√3 units?
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The length of a diagonal of a cube with concutive vertices (3,9) and (...
Let A=(3,9) and B=(3,7),
length of diagonal=√(3-3)²+(9-7)²=√2×2=2units
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The length of a diagonal of a cube with concutive vertices (3,9) and (...
Solution:

Given vertices are (3,9) and (3,7) of a cube.

Finding the length of an edge:

- The given vertices are on the same line parallel to the y-axis.
- Therefore, the distance between them will give the length of an edge.
- Distance between two points (x1, y1) and (x2, y2) is given by the formula √((x2-x1)² + (y2-y1)²).
- The distance between the given vertices is √[(7-9)² + (3-3)²] = √4 = 2 units.

Finding the length of a diagonal:

- In a cube, the length of a diagonal is given by the formula √3 times the length of an edge.
- Therefore, the length of the diagonal is √3 × 2 = 2√3 units.

Hence, the correct option is d. 2√3 units.
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The length of a diagonal of a cube with concutive vertices (3,9) and (3,7) is a. 2 units b. 4 units c. 2√2 units d. 2√3 units?
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