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.
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Answer 1

Answer:

The area of the square field = 5184 sq m.

Each side of the square field = 5184^0.5 = 72 m.

Perimeter of the square field = 4*72 = 288 m.

Perimeter of the rectangular field = 288 m.

Length of the rectangular field is 2B, where B = breadth of the field.

Hence 2(2B+B) = 288, or

3B = 288/2 = 144, or

B = 144/3 = 48 m so length = 2*48 = 96 m.

Area of the rectangular field = 96 * 48 = 4608 sq m.

Answer 2

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The area of a square field is 5184 metre square. 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.

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$\huge\tt{\tt{\color{purple}{\underline{\underline{ꕶolution}}{༉}}}}$

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Given:

• Area of the square field = 5184m².

To Calculate:

• The area of the square field.

How To Find:

First we will calculate the side of the square so as to calculate the perimeter of the square. As it is mentioned in the question, that the perimeter of the given rectangle is equal to the perimeter of the given square.

And after calculating the side of the square, we can hence, be able to find the perimeter of the square.

By applying the formula:

↬ Perimeter (P) = (s + s + s + s)units.

or

↬ Perimeter (P) = (4 × s) units.

where,

• s is the length of each side of the square.

Moreover, we can find the perimeter of a square by adding all its four sides or multiplying the given side by 4 as a square has four equal sides. Since, all sides of a square are equal, therefore, we only need one side to find its perimeter.

Now Calculating:

Area of the square field = 5184m².

To find the side of the square, formula applied:-

${\boxed{\tt{\color {turquoise}{∴ \: ꜱɪᴅᴇ \: ᴏꜰ \: ᴛʜᴇ \: ꜱQᴜᴀʀᴇ \: = \sqrt{ᴀʀᴇᴀ} \: ᴜɴɪᴛꜱ.}}}}$

${\tt{\sf{\color {turquoise}{: \: ⟹ \sqrt{5184 \: m} }}}} \\ {\tt{\color {turquoise}{: \: ⟹}}} \: {\tt{\sf{\underline{\boxed{\color {turquoise}{72 \: m}}}}}}$

Therefore, perimeter of square = (4 × 72)m

⟹ 288m

Know That:

Formula Used to find the perimeter of the rectangle:

↬ 2(l+b) units.

Variables:

• l
• b

where,

• l = length of the rectangle;
• b = breadth of the rectangle.

Now, Let the breadth of the rectangle be x and the length of the rectangle be 2x.

Then we have,

${\tt{\color {turquoise}{→ 2(l + b) = 288m}}} \\ \\ {\tt{\color {turquoise}{→ 2(2x + x) = 288 }}} \\ \\ {\tt{\color {turquoise}{→ x = \frac{288}{6}}}} \\ \\ \: \: \: \: \: \: \: \: \: {\tt{\color {turquoise}{= 48m}}}$

So,

• Length = 2 × 48 = 96m;
• Breadth = 48m

Then, calculating the area of the rectangle:

• Area of the rectangle = (l × b) square units.

After substituting the values:

→ (96 × 48)m²

→ 4608m²

Hence, Area of the rectangle = 4608m².

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