SSC CGL Tier II 12 Jan 2017 Paper 1

Question : 63 of 100

Marks: +1, -0

The sum of the length and breadth of a rectangle is 6 cm. A square is constructed such that one of its sides is equal to a diagonal of the rectangle. If the ratio of areas of the square and rectangle is 5 : 2, the area of the square in cm2 is

20
10
$4 √5$
$10 √2$

Validate

Solution:

(1)

Let, AB = a cm.
BC = b cm.
According to the question,
a + b = 6 ..... (i)
and diagonal of rectangle

= √ { a ^ { 2 } + b ^ { 2 } } =

side of square
∴

{\Area \of \square}/{\Area \of \rectangle}

= { (√ { a ^ { 2 } + b ^ { 2 } } ) ^ { 2 } }/ { a b }

⇒ { 5 }/ { 2 } = { a ^ { 2 } + b ^ { 2 } }/ { a b }

⇒ { 5 } /{ 4 } = { a ^ { 2 } + b ^ { 2 } }/ { 2 a b }

⇒ { 5 + 4 } /{ 5 - 4 } = { a ^ { 2 } + b ^ { 2 } + 2 a b }/ { a ^ { 2 } + b ^ { 2 } - 2 a b }

[By componendo and dividendo]

⇒{ 9 }/ { 1 } = { ( a + b ) ^ { 2 } }/ { ( a - b ) ^ { 2 } }

⇒ { 9 }/ { 1 } = { 6 × 6 } /{ ( a - b ) ^ { 2 } }

⇒ ( a - b ) ^ { 2 } = { 6 × 6 } /{ 9 } = 4

⇒ a – b = 2 ..... (ii)
∴ Area of square

= a ^ { 2 } + b ^ { 2 }

= { 1 } /{ 2 } [ ( a + b ) ^ { 2 } + ( a - b ) ^ { 2 } ]

= { 1 }/ { 2 } ( 36 + 4 )

= { 1 }/ { 2 } × 40 = 20 { \sq. } { \cm }

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