The length of a rectangle is twice the side of a square and its width is $6 c m$ greater than the side of the square. If area of the rectangle is three times the area of the square; find the dimensions of side of square.

Side of square

= 12 c m

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Side of square

= 13 c m

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Side of square

= 18 c m

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None of these

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Solution

The correct option is A Side of square $= 12 c m$
Let side of square $= x c m$
Therefore,
Length of rectangle $= 2 x$
Breadth of rectangle $= x + 6$

According to the question
$2 x (x + 6) = 3 x^{2}$
$=> 2 x^{2} + 12 x - 3 x^{2} = 0$
$=> x^{2} - 12 x = 0$
$=> x^{2} = 12 x$
$=> x = 12$
Therefore,
Side of square $= 12 c m$

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Question 53

Perimeter of a square and a rectangle is same. If a side of the square is 15 cm and one side of the rectangle is 18 cm, find the area of the rectangle.

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The length of a rectangle is twice the side of a square and its width is 6 cm greater than the side of the square. If area of the rectangle is three times the area of the square; find the dimensions of side of square.

The correct option is A Side of square =12 cmLet side of square =x cmTherefore,Length of rectangle =2xBreadth of rectangle =x+6According to the question2x(x+6)=3x2=>2x2+12x−3x2=0=>x2−12x=0=>x2=12x=>x=12Therefore,Side of square =12 cm

The length of a rectangle is twice the side of a square and its width is $6 c m$ greater than the side of the square. If area of the rectangle is three times the area of the square; find the dimensions of side of square.