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Question

The diagonal of a rectangle is thrice its smaller side. Find the ratio of its sides.


A

2:1

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B

22:1

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C

3:2

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D

3:1

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Solution

The correct option is B

22:1


Step 1: Assuming the required measurement

Let ABCD is the rectangle in which AB=a is the longer side and BC=b is the smaller side

According to condition of the question,

The diagonal of a rectangle is thrice its smaller side

We have diagonal AC=3b

Step 2: Finding the ratio

In ABC , B=90° [As each angle of rectangle is of 90°]

Therefore using Pythagoras theorem we have

AC2=AB2+BC2(3b)2=a2+b29b2=a2+b29b2-b2=a28b2=a2a2=8b2a2b2=81ab=81ab=221a:b=22:1AB:BC=22:1

Hence, option (B) is the correct option.


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