Question

The area of a square field is 5184 m². Find the area ofa rectangular field, whose Perimeter
is equal to the Perimeter of the square field and whose length is twice of its breadth.
​

Answer 1

Answer :-

• The area of the rectangular field is 4608 m².

To find :-

• The area of the rectangular field.

Solution :-

• Before finding the area of the rectangular field, let's find it's perimeter first! And for that, we first have to find the perimeter of the square field, for that let's find the length of it's side!

Let :-

• The side of the square field be "x" m.

We know that :-

$\underline{ \boxed{\sf Area \: of \: a \: square = Side \times Side}}$

Here,

• Area = 5184 m².
• Side = "x" m.

Therefore,

$\rm5184 = x \times x$

$\rm5184 = {x}^{2}$

$\rm\sqrt{5184} = x$

$\overline{ \boxed{\rm72 \: m = x}}$

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• Now, let's find the perimeter of the square field!

We know that :-

$\underline{ \boxed{ \sf Perimeter \: of \: a \: square = 4 \times Side}}$

Here,

• Side = 72 m.

Hence,

$\bf Perimeter = 4 \times 72$

$\bf Perimeter = {288 \: m}^{2}$

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• Now, let's find the dimensions of the rectangle!

It is given that :-

• The perimeter of the square field is equal to the perimeter of the rectangular field.

Hence :-

• The perimeter of the rectangular field is 288 m² too.

Let :-

• The breadth of the rectangular field be "x" m.

Then :-

• It's length will be "2x" m.

We know that :-

$\underline{ \boxed{ \sf Perimeter \: of \: a \: rectangle = 2 \: (L + B)}}$

Here,

• Perimeter = 288 m².
• Length = "2x" m.
• Breadth = "x" m.

Substituting the given values in this formula,

$\tt288 = 2 \: (2x + x)$

$\tt288 = 4x + 2x$

$\tt288 = 6x$

$\tt\dfrac{288}{6} = x$

$\tt48 \: m = x$

Therefore, the dimensions of the rectangle are :-

$\bf Length = 2x = 2 \times 48 = 96 \: m.$

$\bf Breadth = x = 48 \: m.$

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• Finally, let's find the area of the rectangular field!

We know that :-

$\underline{ \boxed{ \sf Area \: of \: a \: rectangle = Length \times Breadth}}$

Here,

• Length = 96 m.
• Breadth = 48 m.

Hence,

$\rm Area = 96 \times 48$

$\rm Area = {4608 \: m}^{2}$

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