Question

The area of a square field is 5184msq. 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 . ??

Answer 1

Question:-

The area of a square field is 5184m². 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 . ??

Answer:-

• The area of rectangle is 4608 m².

To find:-

• Area of rectangle

Solution:-

• Area of square = 5184 m²

As we know,

$\large{ \boxed{ \mathfrak{area = {side}^{2} }}}$

Now,

$\large{ \tt : \implies \: \: \: \: \: \: \: \: {side}^{2} = 5184}$

$\large{ \tt : \implies \: \: \: \: \: \: \: \: side = \sqrt{5184} }$

$\large{ \tt : \implies \: \: \: \: \: \: \: \: side = 72}$

• The side of square is 72 m

• Perimeter of square = perimeter of rectangle

As we know,

$\large{ \boxed{ \mathfrak{perimeter \: of \: square = 4 \times side}}}$

Now,

$\large{ \tt : \implies \: \: \: \: \: \: \: \: perimeter = 4 \times 72}$

$\large{ \tt : \implies \: \: \: \: \: \: \: \: perimeter = 288}$

• The perimeter of square is 288 m

In rectangle,

• Length = 2x
• Breadth = x
• Perimeter = 288

As we know,

$\large{ \boxed{ \mathfrak{perimeter = 2(l + b)}}}$

Where,

• l = length of rectangle
• b = breadth of rectangle

Then,

$\large{ \tt : \implies \: \: \: \: \: \: \: \: 2(2x + x) = 288}$

$\large{ \tt : \implies \: \: \: \: \: \: \: \: 3x = \frac{288}{2} }$

$\large{ \tt : \implies \: \: \: \: \: \: \: \: 3x = 144}$

$\large{ \tt : \implies \: \: \: \: \: \: \: \: x = \frac{144}{3} }$

$\large{ \tt : \implies \: \: \: \: \: \: \: \: x = 48}$

• The value of x is 48 m
• Length = 2x = 2×48 = 96 m
• Breadth = x = 48 m

We have to find out the area of rectangle

As we know,

$\large{ \boxed{ \mathfrak{area \: = l \times b}}}$

Where,

• l = length of rectangle
• b = breadth of rectangle

According to question,

$\large{ \tt : \implies \: \: \: \: \: \: \: \: area = 96 \times 48}$

$\large{ \tt : \implies \: \: \: \: \: \: \: \: area = 4608}$

Hence,

• The area of rectangle is 4608 m².

Answer 2

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The area of a square field is 5184m². 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 ?

$\bf {\underline {\underline{✤ ƛƝƧƜЄƦ}}}$

➡Area of rectangular field is 2888m².

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• Area of square field = 5184m²

$\bf {\underline {\underline{✤ ƬƠ \: \: ƇƛLƇƲLƛƬЄ}}}$

• Area of rectangular field

$\bf {\underline {\underline{✤ ƑƠƦMƲLƛ \: \: ƬƠ \: ƁЄ \: \: ƲƧЄƊ}}}$

Area of Square =

$\bf {side}^{2}$

Perimeter of Square =

$\bf4 \times side$

Area of rectangle =

$\bf \: length \times breadth$

Perimeter of rectangle =

$\bf2(lenght + breadth)$

$\bf {\underline {\underline{✤ SƠԼƲƬƖƠƝ}}}$

$\bf Area \: of \: Square \: field = {5184m}^{2}$

$\bf \implies {side}^{2} = 5184$

$\bf \implies side = \sqrt{5184}$

$\bf \implies side = 72m$

$\bf Perimeter \: of \: Square = 4 \times side$

$\bf = 4 \times 72$

$\bf = 288m$

According to question,

Perimeter of square = Perimeter of rectangle

$\bf Perimeter \: of \: rectangle = 2(l + b)$

$\bf \implies 288 = 2(2x + x)$

$\bf \implies 288 = 2 \times 3x$

$\bf \implies 288 \div 2 = 3x$

$\bf \implies 114 = 3x$

$\bf \implies 3x = 114$

$\bf \implies x = 114 \div 3$

$\bf \implies x = 38m$

• Breadth of field = x = 38m
• Length of field = 2x = 2 × 38 = 76m

$\bf area \: of \: rectangular \: field = l \times b$

$\bf = 38 \times 76$

$\bf = 2888 {m}^{2}$

Therefore, Area of rectangular field is 2888m².

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