Find the variance and standard deviation for the following data 65,68,58,44,48,45,60,62,60,50
Answers
Answer:
hlo idbon't have kno w the answersh
Given:
Length of Rectangle = 40 cm
Breadth of rectangle = 10 cm
\sf Area_{\;(square)} = Area_{\;(rectangle)}Area
(square)
=Area
(rectangle)
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To find:
Perimeter of square?
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☯ Let side of square be x cm.
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\begin{gathered}\underline{\bigstar\:\boldsymbol{According\:to\:the\:question\::}}\\ \\\end{gathered}
★Accordingtothequestion:
\sf Area_{\;(square)} = Area_{\;(rectangle)}Area
(square)
=Area
(rectangle)
⠀⠀
We know that,
⠀⠀
\sf Area_{\;(square)} = (side)^2Area
(square)
=(side)
2
\sf Area_{\;(Rectangle)} = length \times breadthArea
(Rectangle)
=length×breadth
⠀⠀
Therefore,
⠀⠀
\begin{gathered}:\implies\sf side \times side = length \times breadth\\ \\\end{gathered}
:⟹side×side=length×breadth
\begin{gathered}:\implies\sf x \times x = 40 \times 10\\ \\\end{gathered}
:⟹x×x=40×10
\begin{gathered}:\implies\sf x^2 = 400\\ \\\end{gathered}
:⟹x
2
=400
\begin{gathered}:\implies\sf \sqrt{x^2} = \sqrt{400}\qquad\quad\bigg\lgroup\bf Squaring\;both\;sides \bigg\rgroup\\ \\\end{gathered}
:⟹
x
2
=
400
⎩
⎪
⎪
⎪
⎧
Squaringbothsides
⎭
⎪
⎪
⎪
⎫
\begin{gathered}:\implies{\underline{\boxed{\frak{\purple{x = 20}}}}}\;\bigstar\\ \\\end{gathered}
:⟹
x=20
★
\therefore\;{\underline{\sf{Side\;of\;square\;is\;{\textsf{\textbf{20\;cm}}}.}}}∴
Sideofsquareis20cm.
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Now, Finding Perimeter of square,
⠀⠀
\begin{gathered}\dag\;{\underline{\frak{As\;we\;know\;that,}}}\\ \\\end{gathered}
†
Asweknowthat,
\begin{gathered}\star\;{\boxed{\sf{\pink{Perimeter_{\;(square)} = 4 \times side}}}}\\ \\\end{gathered}
⋆
Perimeter
(square)
=4×side
\begin{gathered}:\implies\sf Perimeter_{\;(square)} = 4 \times 20\\ \\\end{gathered}
:⟹Perimeter
(square)
=4×20
\begin{gathered}:\implies{\underline{\boxed{\frak{\purple{Perimeter_{\;(square)} = 80\;cm}}}}}\;\bigstar\\ \\\end{gathered}
:⟹
Perimeter
(square)
=80cm
★
\therefore\;{\underline{\sf{Perimeter\;of\;square\;is\;{\textsf{\textbf{80\;cm}}}.}}}∴
Perimeterofsquareis80cm.
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\begin{gathered}\qquad\qquad\boxed{\underline{\underline{\pink{\bigstar \: \bf\:Formulas\:related\:to\:it\:\bigstar}}}} \\ \\\end{gathered}
★Formulasrelatedtoit★
\begin{gathered}\begin{array}{|c|c|c|}\cline{1-3}\bf Shape&\bf Area\ formula&\bf Perimeter\ formula\\\cline{1-3}\sf Square&\tt side \times side}&\tt 4 \times side\\\cline{1-3}\sf Rectangle&\tt length \times breadth&\tt 2(length + breadth)\\\cline{1-3}\sf Triangle&\tt \dfrac{1}{2} \times base \times height&\tt sum\of\ all\ sides\ of\ \triangle\\\cline{1-3}\end{array}\end{gathered}