The diagonal of a rectangle is thrice the length of its smaller side. What is the ratio of its length and breadth?


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Answer:

2√2:1

Step by Step Explanation:

  1. Let us assume that ABCD is a rectangle.
  2. Let b and l be the breadth(smaller side) and length of the rectangle, respectively.
    Since, the diagonal of the rectangle is thrice the length of its smaller side.
    Therefore, the length of the diagonal = 3b cm.
  3. On looking at the rectangle ABCD carefully, we notice that ABC is a right angled triangle where AB, BC, and AC are the breadth, length, and diagonal of the rectangle, respectively.
    Now, in the right angled triangle ABC,
    AC2 = AB2 + BC2
    ⇒ (3b)2 = b2 + l2
    ⇒ 9b2 - b2 = l2
    ⇒ (9 - 1)b2 = l2
    ⇒ 8b2 = l2
    ⇒ l2 = 8b2
    ⇒  
    l2
    b2
      =  
    8
    1
     
    ⇒ ( 
    l
    b
     )2 =  
    8
    1
     
    ⇒  
    l
    b
      =  
    2√2
    1
     
    ⇒ l:b = 2√2:1
  4. Therefore, we can say that the ratio of the length and breadth of the rectangle is 2√2:1.

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