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

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

1. A

2:1

2. B

√2 :1

3. C

2√2 :1

4. D

1:2

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### Solution:

Let AD = x cm and diagonal BD = 3x cm.

In right-angled triangle DAB,

AD2 + AB2 = BD2 (Using Pythagoras Theorem)

x2 + AB2 = (3x)2

⇒ x2 + AB2 = 9x2

⇒ AB2 = 9x2 – x2

⇒ AB2 = 8x2

⇒ AB = √8x = 2√2x

Required ratio of AB : AD = 2√2x : x = 2√2 : 1

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