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: $\sqrt5: 1$
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Correct Answer: $\sqrt{15 } : 1$
Solution : Diagonal = 4 × breadth Diagonal2 = length2 + breadth2 ⇒ (4 × breadth)2 = length2 + breadth2 ⇒ Length2 = 15 × breadth2 ⇒ Length = $\sqrt{15}$ × breadth ⇒ Length : Breadth = $\sqrt{15} : 1$ Hence, the correct answer is $\sqrt{15} : 1$.
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