Question

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

Answer 1

Step-by-step explanation:

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. What is the area of the rectangular field?

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Hungenahalli Sitaramarao Badarinath, Ph.D. in Civil Engineering. Maths keeps one mentally active.

Answered June 30, 2018

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

$the \: area \: of \: square \: is=5184m²$

$\therefore \: {s}^{2} =5184m²$

$= > s = \sqrt{5184 {m}^{2} }$

$= > s = 72m$

Let Breadth of Rectangle=x m

∴ Length Of the Rectangle= 2x m

According to the Question

Perimeter of Rectangle = Perimeter of Square

$2(2x + x) = 4 \times 72$

$= > 6x = 288m$

$= > x = \frac{288}{6} = 48m$

$∴length = 2 \times 48 = 96m$

$breadth = 48m$

$\therefore \: area \: of \: rectangle   =l×b=96m×48m$

$= > 4608 {m}^{2}$