Question

The area of a square field is 5184 m². A rectangular field, whose length is twice its
breadth, has its perimeter equal to the perimeter of the square field. Find the area
of the rectangular field.
by prime factorisation
​

Answer 1

Answer :-

• The area of the rectangular field is 4806 m².

Step-by-step explanation :-

• To solve this question, we first have to find the length of each side of the square using it's area. Then we will find it's perimeter. It has been given that the perimeter of the rectangular field is equal to the perimeter of the square. Using this information, we will form an equation and solve it to find out our answer!

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Finding the length of each side of the square field :-

We know that :-

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

Here,

• Area of the field = 5184 m².

Hence,

$\bf 5184 = Side \times Side$

Multiplying side with side,

$\bf 5184 = Side^2$

Now let's find the square root of 5184.

$\bf \sqrt{5184} = Side$

Finding the square root of 5184,

$\overline{\boxed{\bf 72 \: m = Side}}$

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Finding the perimeter of the square field :-

We know that :-

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

Here,

• Side = 72 m.

Hence,

$\bf Perimeter = 4 \times 72$

Multiplying the numbers,

$\overline{\boxed{\bf Perimeter = 288 \: m}}$

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Finding the dimensions of the rectangular field :-

• Let the breadth of the field be "x".

• As the length of the field is twice it's breadth, it will be "2x".

• It has been given that the perimeter of the square field is equal to that of the rectangular field. So it's perimeter is 288 m too.

Now, we know that :-

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

Here,

• Length = 2x.
• Breadth = x.

Hence,

$\rm 288 = 2 \: (2x + x)$

Adding x to 2x,

$\rm 288=2\:(3x)$

Removing the brackets,

$\rm 288 = 2\times 3x$

Multiplying 2 with 3x,

$\rm 288 = 6x$

Transposing 6 from RHS to LHS, changing it's sign,

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

Dividing 288 by 6,

$\overline{\boxed{\rm 48 \: m = x}}$

• The value of x is 48 m.

Hence, the dimensions of the rectangular plot are as follows :-

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

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

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Finding 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,

$\rm Area = 96 \times 48$

Multiplying the numbers,

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

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Abbreviations used :-

L = Length.

B = Breadth.

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Note :- Kindly view the attachment to understand how to find the square root of 5184 by prime factorisation.

Answer 2

Answer:

Area of rectangular field = 4608m²

Step-by-step explanation:

Area of square = a² [a = length of side]

Perimeter of square = 4a

Area of rectangle = l×b [l = length; b = breadth]

Perimeter of rectangle = 2(l+b)

According to the question,

Area of square field = 5184m²

=> a² = 5184

=> a = ✓5184

=> a = 72m.

Perimeter of square field

= 4a

= 4×72

= 288m

Again, According to question,

Perimeter of rectangular field = Perimeter of square field

=> 2(l+b) = 288

=> 2(2b+b) = 288 [Given: length of rectangular field is equal to twice its breadth]

=> 2×3b = 288

=> 6b =288

=> b = 48m

Therefore,

l = 2b

= 2×48

= 96m

Thus, Area of rectangle

= l×b

=96×48

= 4608m²

Hope this helps!