Question

A rectangle has twice the area of square . The length of rectangle is 12 cm greater and width Is 8 cm greater than a side of a square . Find the perimeter of square

Answer 1

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Answer 2

For the given square, the perimeter will be 96 cm.

Given,

Area of a rectangle = twice the square area.

The length and breadth of the rectangle are 12 cm and 8 cm respectively more than the side of the square.

To find,

The perimeter of the square.

Solution,

Firstly, let the given square has a side x cm, and $l, b$ be the length and breadth of the rectangle, respectively.

Now, according to the given condition,

$l$ = x + 12,

$b$ = x + 8.

Since we know, the area of a rectangle is $= l \times b$.

For the given rectangle, area,

$A_r=(x+12)(x+8)\\\implies A_r = x^{2} +20x+96$

Further, we know that the area of a square is $(side)^{2}$.

So, for the given square, area,

$A = x^{2}$

Here, it is given that the rectangle has twice the area of the square.

So,

$A_r=2A$

$\implies x^{2} +20x+96=2x^{2}$

$\implies x^{2} -20x-96=0$

Solving the above quadratic equation using factorization,

$\implies x^{2} +(-24+4)x-96=0$

$\implies x^{2} -24x+4x-96=0$

$\implies x(x -24)+4(x-24)=0$

$\implies (x+4)(x -24)=0$

⇒ x = -4 or x = 24.

Since we have assumed x to be the side of a square, only x = 24 shall be considered, as a dimension cannot be negative.

Hence, for the given square,

side = x = 24 cm.

Finally, we know that the perimeter of a square $=4 \times side$ = 4x.

Thus, for the given square, x = 24 cm,

Perimeter = 4×24 = 96 cm.

⇒ Perimeter of the square = 96 cm.

Therefore, for the given square, the perimeter will be 96 cm.

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