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If the diagonals of a rectangle are 10 cm long, what is the length of each side

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Question: If the diagonals of a rectangle are 10 cm long, what is the length of each side if the rectangle is a square?

Options:

  1. 5 cm
  2. 10 cm
  3. 7.07 cm
  4. 8 cm

Correct Answer: 7.07 cm

Solution: 

In a square, the diagonal d is related to the side length s by the formula d = s√2. Therefore, s = d/√2 = 10 cm/√2 = 10 cm/1.414 ≈ 7.07 cm.

If the diagonals of a rectangle are 10 cm long, what is the length of each side

Practice Questions

Q1
If the diagonals of a rectangle are 10 cm long, what is the length of each side if the rectangle is a square?
  1. 5 cm
  2. 10 cm
  3. 7.07 cm
  4. 8 cm

Questions & Step-by-Step Solutions

If the diagonals of a rectangle are 10 cm long, what is the length of each side if the rectangle is a square?
  • Pythagorean Theorem – The relationship between the sides of a right triangle, which is applied here to find the side length of a square using its diagonal.
  • Properties of Squares – Understanding that a square is a specific type of rectangle where all sides are equal.
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