Question

the area of square field is 5184 square meter find the area rectangular Field whose perimeter is equal to the perimeter of square field and whose length is twice of its breadth​

Answer 1

Answer:1296 if I’m not wrong please

Step-by-step explanation:

Answer 2

Step-by-step explanation:

Appropriate Question :

• The area of square field is 5184m². Find the area of the rectangular field whose perimeter is equal to the perimeter of square field and whose length is twice of its breadth.

$\frak{\red{Given}} \begin{cases} & \sf {Area\ of\ the\ square\ field\ is\ 5184m^2.} \\ & \sf {Perimeter\ of\ rectangular\ field\ is\ equal\ to\ perimeter\ of\ square\ field.} \\ & \sf {Length\ of\ the\ rectangular\ field\ is\ twice\ to\ the\ breadth\ of\ the\ square\ field.} \end{cases}$

Need to find : We have to find the area of the rectangular field.

• We are given the area of the square field, that is 5184m². So firstly, let us find out the side of the square field.

Let the side of the square field be a.

SidE :-

• a² = 5184m²
• a = √5184m
• a = 2 × 2 × 2 × 9
• a = 72m

∴ Hence, the side of the square field is 72m. Now, let's find out the perimeter of square.

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$\red \bigstar \sf{\underline{Finding\ perimeter\ of\ square:-}}$

$\sf \dashrightarrow {Perimeter\ of\ square\ =\ 4a} \\ \\ \sf \dashrightarrow {4 \times 72} \\ \\ \dashrightarrow {\underline{\boxed{\purple{\frak{288m}}}}}$

∴ Hence, the perimeter of the square field is 288m. Now, let us find out the length and breadth of the rectangular field.

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• Since, it is given that perimeter of the rectangular field is equal to the perimeter of square field. Also, the length of the rectangular field is twice the breadth of the square field.

$\sf : \implies {Perimeter\ of\ rectangle\ =\ Perimeter\ of\ square} \\ \\ \sf : \implies {2(l\ +\ b)\ =\ 288} \\ \\ \sf : \implies {2(2b\ +\ b)\ =\ 288} \\ \\ \sf : \implies {4b\ +\ 2b\ =\ 288} \\ \\ \sf : \implies {6b\ =\ 288} \\ \\ \sf : \implies {b\ =\ \dfrac{\cancel{288}}{\cancel{6}}} \\ \\ : \implies {\underline{\boxed{\purple{\frak{b\ =\ 48m}}}}}$

∴ Hence, breadth of the rectangular field is 48m. Now, let's find out the length of the rectangular field.

LengtH :-

• 2(48)
• 2 × 48
• 96m

∴ Hence, the length of the rectangular field is 96m. Now, let's find out the area of the rectangular field.

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$\red \bigstar \sf{\underline{Finding\ area\ of\ the\ rectangular\ field:-}}$

$\sf : \implies {Area\ of\ rectangle\ =\ l \times b} \\ \\ \sf : \implies {Area\ of\ rectangle\ =\ 96 \times 48} \\ \\ : \implies {\underbrace{\boxed{\pink{\frak{Area\ of\ rectangle\ =\ 4608m^2}}}}_{\sf \blue{\tiny{Area\ of\ the\ field}}}}$

∴ Hence, area of the rectangular field is 4608m².