Question

area of a square field is equal to the area of a rectangular field which is 24 metre and 15 metre find the length of the side of a square​

Answer 1

Answer:

⋆ DIAGRAM :

$\setlength{\unitlength}{1.3cm}\begin{picture}(20,2)\thicklines\put(7.3,2){\sf{\large{15 m}}}\put(9.2,0.7){\sf{\large{24 m}}}\put(8,1){\line(1,0){3}}\put(8,1){\line(0,2){2}}\put(11,1){\line(0,3){2}}\put(8,3){\line(3,0){3}}\put(12.7,0.7){\sf{\large{? m}}}\put(12,1){\line(1,0){2}}\put(12,1){\line(0,2){1.5}}\put(14,1){\line(0,3){1.5}}\put(12,2.5){\line(3,0){2}}\put(8.5,1.8){\Large\bf Rectangle}\put(12.5,1.6){\bf Square}\end{picture}$

$\rule{150}{1}$

$\underline{\bigstar\:\:\textsf{According to the Question :}}$

$\dashrightarrow\tt\:\:Area\:of\:Square=Area\:of\:Rectangle\\\\\\\dashrightarrow\tt\:\:(Side)^2=(Length\times Breadth)\\\\\\\dashrightarrow\tt\:\:(Side)^2=(24\:m \times 15\:m)\\\\\\\dashrightarrow\tt\:\:Side = \sqrt{24 \:m \times 15\:m}\\\\\\\dashrightarrow\tt\:\:Side = \sqrt{(4 \times 2 \times 3)\:m \times (5 \times 3)\:m}\\\\\\\dashrightarrow\tt\:\:Side = \sqrt{(3 \times 3) \times (2 \times 2) \times 2 \times 5\times m^2}\\\\\\\dashrightarrow\tt\:\:Side = 3 \times 2 \sqrt{2 \times 5}\:m\\\\\\\dashrightarrow\:\:\underline{\boxed{\tt Side = 6 \sqrt{10}\:m}}$

⠀

$\therefore\:\underline{\textsf{Side of the Square will be \textbf{6 \sqrt{\text{10}} m}}}.$

Answer 2

Given:-

• Area of square = Area of rectangle
• Length of rectangle = 24 m
• Breadth of rectangle = 15 m

To find:-

• Side of square = ?

Solution:-

⋆ DIAGRAM OF RECTANGLE :-

$\setlength{\unitlength}{0.78 cm}\begin{picture}(12,4)\thicklines\put(5.6,9.1){ A }\put(5.5,5.8){ B }\put(11.1,5.8){ C }\put(11.05,9.1){ D }\put(4.5,7.5){ 15\:m }\put(8.1,5.3){ 24 \:m }\put(11.5,7.5){ 15 \:m }\put(8.1,9.5){ 24\:m }\put(6,6){\line(1,0){5}}\put(6,9){\line(1,0){5}}\put(11,9){\line(0,-1){3}}\put(6,6){\line(0,1){3}}\end{picture}$

Now we know,

$\star\:{\boxed{\sf\blue{Area \: of \: rectangle = Length \times Breadth }}}$

$\longrightarrow\sf Area \: of \: rectangle = (24 \times 15)\: m^2 \\\\\longrightarrow\sf\green{ Area \: of \: rectangle = 360 \: m^2 }$

$\rule{200}{1}$

⋆ DIAGRAM OF SQUARE:-

$\setlength{\unitlength}{1.05 cm}}\begin{picture}(12,4)\thicklines\put(5.6,9.1){ A }\put(5.6,5.8){ B }\put(9.1,5.8){ C }\put(9.05,9.1){ D }\put(4.5,7.5){ a\:cm }\put(7.1,5.3){ a\:m }\put(9.5,7.5){ a \:m }\put(7.1,9.5){ a \:m }\put(6,6){\line(1,0){3}}\put(6,9){\line(1,0){3}}\put(9,9){\line(0,-1){3}}\put(6,6){\line(0,1){3}}\end{picture}$

We also know,

$\star\: {\boxed{\sf\red{Area \: of \: square = (Side)^2 }}}$

${\underline{\bigstar{\textsf{\: According to Question : —}}}} \\\\\longrightarrow\sf Area_{rectangle} = Area_{Square} \\\\\longrightarrow\sf 360 = (Side)^2 \\\\\longrightarrow\sf Side = \sqrt{360} \\\\\longrightarrow\underline{\boxed{\sf\blue{Side_{Square} = 18.97 \: m }}}\: \: \star\\\\\\\therefore\underline{\textsf{Side of square = {\textbf{18.97 m }}}}$