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What is the longest distance between two points in a rectangular solid if the area of its faces is 50, 75 and150 square units respectively?
  • a)
    5√14
  • b)
    3√70
  • c)
    10√7
  • d)
    14√5
  • e)
    Cannot be determined
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
What is the longest distance between two points in a rectangular solid...
Given
  • Area of faces of a rectangular solid:
    • Face -1 = 50 square units
    • Face-2 = 75 square units
    • Face-3 = 150 square units
To Find: Length of the longest distance between two points inside the solid.
Approach
  1.     Length of the longest distance between 2 points inside the solid = (length of the space diagonal) = So, we need to find the dimensions of the rectangular solid
  2. Let’s assume the length, breadth and height of the rectangular solid be l, b and h respectively.
    So, we have
    1. l * b = 50……..(1)
    2. b * h = 75 ……(2)
    3. l * h = 150……(3)
  3. As we have 3 equations and 3 unknowns we will solve the above equations to find the value of l, b and h.
Working Out
  1. Multiplying (1), (2) and (3), we have 
 
  1. Substituting equation (1) in (4), we have, h = 15
     
  2. Substituting equation (2) in (4), we have, l = 10
     
  3. Substituting equation (3) in (4), we have, b = 5
 2. Length of space diagonal = 
Answer: A
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What is the longest distance between two points in a rectangular solid if the area of its faces is50, 75 and150 square units respectively?a)5√14b)3√70c)10√7d)14√5e)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer?
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