A square carpet when placed in a room leaves a strip $1 m$ wide uncarpeted along one pair of opposite walls and a strip $2 m$ wide along the other two walls. If the area uncarpeted is $62 s q m$ , what is the length of the carpet?

10 m

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9 m

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8 m

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7 m

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Solution

The correct option is B $9 m$
Let the side of the carpet be $x$ m.
Then as per the figure, the length of the sides of the room $= x + 4; x + 2$
Given, area of the uncarpeted area $= 62 s q m$
$=> (x + 4) (x + 2) - x^{2} = 62$
$=> x^{2} + 4 x + 2 x + 8 - x^{2} = 62$
$=> 6 x + 8 = 62$
$=> 6 x = 54$
$=> x = 9$
Hence, the length of the carpet $= 9 m$

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A square carpet when placed in a room leaves a strip 1m wide uncarpeted along one pair of opposite walls and a strip 2m wide along the other two walls. If the area uncarpeted is 62sqm, what is the length of the carpet?

The correct option is B 9mLet the side of the carpet be x m. Then as per the figure, the length of the sides of the room =x+4;x+2 Given, area of the uncarpeted area =62sqm=>(x+4)(x+2)−x2=62=>x2+4x+2x+8−x2=62=>6x+8=62=>6x=54 =>x=9 Hence, the length of the carpet =9m

A square carpet when placed in a room leaves a strip $1 m$ wide uncarpeted along one pair of opposite walls and a strip $2 m$ wide along the other two walls. If the area uncarpeted is $62 s q m$ , what is the length of the carpet?