Question

The perimeter of a rectangular sheet is 100cm the Length of the sheet is 40cm! find the breadth and the area of it​

Answer 1

${\large{\underline{\pmb{\frak{Given :}}}}}$

★ The measure of the perimeter of a rectangular sheet is 100cm

★ The measure of the length of the sheet is 40cm

${\large{\underline{\pmb{\frak{To \; Find:}}}}}$

★ The measure of the area of the rectangle is the given units

★ The measurement of the breadth of the rectangular sheet

${\large{\underline{\pmb{\frak{Understanding \; the \; Concept:}}}}}$

❍ Concept : Here wee have been said that  the perimeter of the rectangular sheet is 100cm and been provided with the measure of one of its dimensions which is that the length measures 40cm and that we should find the measure of breadth of the rectangle and it's area

✰  As we have the measure of the perimeter and the length of the rectangular shaped sheet so now let's use suitable formulae to find the measure of the breadth of the rectangular sheet and its area

${\large{\underline{\pmb{\frak{Using \; Concepts:}}}}}$

✪ Formula to find the perimeter of a rectangle :

$\tt Perimeter \; of \; a \; rectangle = 2(L+B)$

✪ Formula to find the area of a rectangle:

$\tt Area \; of \; a \; rectangle = L \times B$

${\large{\underline{\pmb{\sf{RequirEd \; Solution:}}}}}$

→ The area and the breadth of the rectangular sheet are 400cm² and 10cm respectively

${\large{\underline{\pmb{\frak{Full \; solution:}}}}}$

~ Now as we know that the perimeter of the rectangle is 100cm so, let's use the above mentioned formula and find the breadth of the rectangle so that we can find the area

${:\implies}\sf Perimeter \; of \; a \; rectangle = 2 ( L+ B )$

${:\implies}\sf 100cm = 2( 40cm + B )$

${:\implies}\sf 100cm = 80cm + 2 b$

${:\implies}\sf 2b = 100cm - 80cm$

${:\implies}\sf 2b = 20cm$

${:\implies}\sf b = 20cm/2$

${:\implies}\sf b = 10cm$

• Henceforth the breadth of the rectangle is 10cm

~ Now as we have found out the breadth of the rectangle let's find the area using the length and the breadth of the rectangle

${:\implies}\sf Area \; of \; a\; rectangle = L \times B$

${:\implies}\sf Area \; of \; the\; rectangle = 40cm \times 10cm$

${:\implies}\sf Area \; of \; the\; rectangle = 400cm^2$

• Henceforth the area of the rectangle is 400cm²

${\large{\underline{\pmb{\frak{Diagrams :}}}}}$

→ For web users :

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large 40 cm}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large 10 cm}\end{picture}$

→ For app  users :

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered} \: \: \: \sf{10cm \: \: }\boxed{\begin{array}{cc} \\ \\\\ \sf\green{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\:\:\:\:\:\:}\\ \end{array}} \\ \sf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 40cm}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$

See this question at : https://brainly.in/question/41210900

Answer 2

Answer:

• The breadth of the rectangular sheet = 10cm
• The area of the rectangular sheet = 400cm²

Step-by-step explanation:

$\frak {Given} = \begin{cases} &\sf{The\:perimeter\:of\:the\:rectangular\:sheet\:=100cm} \\\\\\\\\\ & \sf{The\:length\:of\:the\:rectangular\:sheet\:=40cm}\end{cases}$

To find:-  

• The breadth of the rectangular sheet
• The area of the rectangular sheet

Solution:-

Firstly we have to find the breadth of the rectangular sheet.

$\qquad\sf{\implies\:The\:perimeter\:of\:the\:rectangular\:sheet\:=2\:(\:Length\:+\:Breadth\:)}$

$\qquad\sf{\implies\:100\:=2\:(\:40\:+\:Breadth\:)}$

$\qquad\sf{\implies\:\dfrac{100}{2}\:=\:(\:40\:+\:Breadth\:)}$

$\qquad\sf{\implies\:50\:=\:(\:40\:+\:Breadth\:)}$

$\qquad\sf{\implies\:50\:-\:40\:=\:Breadth}$

$\qquad\sf{\implies\:10cm\:=\:Breadth\:}$

$\qquad\qquad\color{lime}{\sf{\underline{Therefore\:the\:breadth\:of\:the\:rectangular\:sheet\:is\:10cm.}}}$

_______________________________

Now we have to find the area of  the rectangular sheet

• Length = 40cm
• Breadth = 10cm

$\qquad\sf{\implies\:The\:area\:of\:the\:rectangular\:sheet\:=\:Length\:\times\:Breadth }$

$\qquad\sf{\implies\:The\:area\:of\:the\:rectangular\:sheet\:=\:40\:\times\:10}$

$\qquad\sf{\implies\:The\:area\:of\:the\:rectangular\:sheet\:=\:400cm^{2} }$

$\qquad\qquad\color{orange}{\sf{\underline{Therefore\:the\:area\:of\:the\:rectangular\:sheet\:is\:400cm^{2}.}}}$