Question

The area of square field is 8184 m.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 rectangular field.

Answer 1

Correct Question:-

• The area of 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 rectangular field.

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GivEn:-

• Area of square field = 5184m²

• Length of Rectanglular field is twice its breadth.

• Perimeter of Rectanglular field is equals to perimeter of the square field.

To find:-

• Area of Rectangular field.

SoluTion:-

Area of square field = 5184m²

As we know that,

$\dag\;{\underline{\boxed{\bf{Area\;of\;square\;=\;(Side)^2}}}}$

$\therefore\sf (side)^2 = 5184\;m^2$

$\;\;\;\;\small\sf\dag\;{\underline{Taking\;sqrt\;both\;sides:-}}$

$:\implies\sf \sqrt{(side)^2} = \sqrt{5184}$

$:\implies\bf side = 72\;m$

✩ SQUARE

$\setlength{\unitlength}{1.5cm}\begin{picture}(8,2)\thicklines\put(7.7,3){\large{A}}\put(7.2,2){\mathsf{\large{72 cm}}}\put(7.7,1){\large{B}}\put(9,0.7){\matsf{\large{72 cm}}}\put(10.6,1){\large{C}}\put(8,1){\line(1,0){2.5}}\put(8,1){\line(0,2){2}}\put(10.5,1){\line(0,3){2}}\put(8,3){\line(3,0){2.5}}\put(10.6,3){\large{D}}\end{picture}$

$\dag\;{\underline{\underline{\bf{\pink{According\;to\;question:-}}}}}$

☯ Length of Rectanglular field is twice its breadth.

★ Lets Breadth of Rectangle = x m

$\therefore$ Length of rectangle = (2x) m

✩ RECTANGLE

$\setlength{\unitlength}{1.5cm}\begin{picture}(8,2)\linethickness{0.4mm}\put(7.7,3){\large\sf{A}}\put(7.5,2){\sf{\large{x}}}\put(7.7,1){\large\sf{B}}\put(9.3,0.7){\sf{\large{2x}}}\put(11.1,1){\large\sf{C}}\put(11.1,3){\large\sf{D}}\put(8,1){\line(1,0){3}}\put(8,1){\line(0,2){2}}\put(11,1){\line(0,3){2}}\put(8,3){\line(3,0){3}}\end{picture}$

Now,

☯ Perimeter of rectangle = Perimeter of a square

$:\implies$ 2(l + b) = 288m

$:\implies$ 2(2x + x) = 288m

$:\implies$ 4x + 2x = 288m

$:\implies$ 6x = 288m

$:\implies\sf x = \dfrac{288}{6}$

$:\implies\bf x = 48\;m$

Therefore,

• Length of Rectangular field = 2x m = 2 × 48 = 96m

• Breadth of Rectangular field = x m = 48m

As we know that,

$\dag\;{\underline{\boxed{\bf{Area\;of\;Rectangle\;=\;l \times b}}}}$

$:\implies$ l × b

$:\implies$ 96 × 48

$:\implies{\underline{\boxed{\bf{\blue{4608\;m^2}}}}}$ ★

$\dag$ Hence, Area of Rectanglular field is 4608m².

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