Question : In a rectangle, the diagonal is 4 times its breadth. The ratio of length to breadth is:
Option 1: $\sqrt{15 } : 1$
Option 2: $\sqrt1: 5$
Option 3: $1: 5$
Option 4: $\sqrt5: 1$
Correct Answer: $\sqrt{15 } : 1$
Solution :
Diagonal = 4 × breadth
Diagonal
2
= length
2
+ breadth
2
⇒ (4 × breadth)
2
= length
2
+ breadth
2
⇒ Length
2
= 15 × breadth
2
⇒ Length = $\sqrt{15}$ × breadth
⇒ Length : Breadth = $\sqrt{15} : 1$
Hence, the correct answer is $\sqrt{15} : 1$.
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