Question

The area of square field is 5184m^2.Find the area of rectangular field,whose perimeter is equal to perimeter of square field and whose length is twice of its breath.

Answer 1

$<b>Heya mate. (^_-). Solution below.$
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$<u>Your Question -</u>$

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 its breadth.

$<u>Solution -</u>$

Area of the square field = 5184 m² (as given in the question)

But, area of any square = a², where a is a side of the square

Then,

a² = 5184 m²

=> a = √5184 m²

=> a = √(72 m × 72 m)

=> a = 72 m

Hence, the side of the square field measures 72 m.
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Now, Perimeter of the square field

= 4 × a

= 4 × 72m

= 288 m $\mathcal{\bold{(Equation\:i)}}$
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Now, coming to the rectangle field,

Let the breadth (b) be 'x'.

Then, the length (l)
= 2 times breadth
= 2 × x
= 2x

So, the perimeter of the rectangle field -

= 2 (l + b)

= 2 (x + 2x)

= 2 (3x)

= 6x. $\mathcal{\bold{(Equation\: ii)}}$
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But, the perimeter of the square field = the length of the rectangle field (as per the question)

Then, by Equation i and ii,

288m = 6x

=> 288m/6 = x

=> 48m = x

=> x = 48 m

So, breadth = x = 48 m.
Length = 2x = 2 × 48 = 96 m.

$<marquee>Therefore, the length of the rectangular field = 96 m.$

$And, the breadth of the rectangular field = 48 m.</marquee>$
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Thank you.. ;-)