Question

the area of a rectangle is 650 cm square and breadth is 13 find its length and perimeter​

Answer 1

Answer:

• Length of the rectangle = 50 cm
• Perimeter = 126 cm

Step-by-step explanation:

GIVEN :-

• Area of the rectangle = ${650 \: cm}^{2}$
• Breadth of the rectangle = $13 \: cm$

TO FIND :-

• Length of the rectangle
• Perimeter of the rectangle

FORMULA USED :-

• Area of rectangle = Length X Breadth
• Perimeter of rectangle = 2(Length + Breadth)

SOLUTION :-

• For length of the rectangle :-

$Area \: of \: rectangle = Length \times Breadth \\ \\ => \: 650 = length \times 13 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ => \: length = \frac{650}{13} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ => \: 50cm \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

• For perimeter of the rectangle :-

$Perimeter \: of \: rectangle = 2(Length \times Breadth) \\ \\ =>\: 2(50 + 13) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ => \: 2 \times 63 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ => \: 126 \: cm \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

So, length of the rectangle is 50 cm and perimeter is 126 cm.

FORMULAS :-

• $Area \: of \: rectangle = l \times b$
• $Perimeter \: of \: rectangle = 2(l + b)$
• $Diagonal \: of \: rectangle = \sqrt{ {l}^{2} + {b}^{2} }$
• $Area \: of \: square = {a}^{2}$
• $Perimeter \: of \: square = 4a$
• $Diagonal of square = \sqrt{2} a$
• $Side \: of \: square = \frac{p}{4}$

Here,

• l = length
• b = bredth
• p = perimeter

Answer 2

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large 50 cm}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large 13 cm}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture}$

$\LARGE\textbf{\underline{\underline{Answer :- }}}$

$\large\textsf{↣ Length of the rectangle = 50 cm}$

$\large\textsf{↣ Perimeter of the rectangle = 126 cm}$

$\LARGE\textbf{\underline{\underline{Given :- }}}$

$\large\textsf{⇝ Area of the rectangle = 650 cm²}$

$\large\textsf{⇝ Breadth of the rectangle = 13 cm}$

$\LARGE\textbf{\underline{\underline{To find :- }}}$

$\large\textsf{↣ Length of the rectangle = ?}$

$\large\textsf{↣ Perimeter of the rectangle = ?}$

$\LARGE\textbf{\underline{\underline{Formula :- }}}$

$\large\boxed{\textsf\textcolor{purple}{༒ Perimeter of the rectangle = 2 ( l + b )}}$

$\large\boxed{\textsf\textcolor{purple}{༒ Area of the rectangle = l × b }}$

$\LARGE\textbf{\underline{\underline{How to solve :- }}}$

• First using the formula of ' Area of the rectangle ' we have the find the length of the rectangle.

• Then once we find the length of the rectangle we can easily find the ' Perimeter of the rectangle' .

$\LARGE\textbf{\underline{\underline{Solution :- }}}$

• ❶ Finding the length of the rectangle with the help of the formula of the area of the rectangle .

• Area of the rectangle = 650 cm²

• Breadth of the rectangle ( b ) = 13 cm .

• Length of the rectangle ( l ) = ?

$\large\textsf{⟾ 650 = 13 × l }$

$\large\textsf{⟾ \cfrac{650}{13} = l }$

$\large\textsf{⟾ \cancel\cfrac{650}{13} = l }$

$\large\textsf{⟾ 50 = l }$

$\large\boxed{\therefore\textsf\textcolor{magenta}{Length of the rectangle = 50 cm}}$

• ❷ Calculating the perimeter of the rectangle with the help of the ' length of the rectangle ' calculated above .

• Length of the rectangle = 50 cm

• Breadth of the rectangle = 13 cm .

• Perimeter of the rectangle = ?

$\large\textsf{⟾ Perimeter = 2 ( 50 + 13 ) }$

$\large\textsf{⟾ Perimeter = 2 ( 63 ) }$

$\large\textsf{⟾ Perimeter = 126 cm}$

$\large\boxed{\therefore\textsf\textcolor{magenta}{Perimeter of the rectangle = 126 cm .}}$

$\LARGE\textbf{\underline{\underline{* Note :- }}}$

⇝ I have drawn a figure and it is visible only from the web version.....so see the answer from the web version.....

$\LARGE\textbf{\underline{\underline{More Formulas :-}}}$

$\large\boxed{\textbf\textcolor{green}{↦ Area of a rectangle = l × b .}}$

$\large\boxed{\textbf\textcolor{green}{↦ Perimeter of the rectangle = 2 ( l + b ) .}}$

$\large\boxed{\textbf\textcolor{green}{↦ Diagonal of the rectangle = \sqrt{ l^{2} + b^{2}} }}$

$\large\boxed{\textbf\textcolor{red}{↦ Area of the square = Side² .}}$

$\large\boxed{\textbf\textcolor{red}{↦ Perimeter of the rectangle = 4 × Side .}}$

$\large\boxed{\textbf\textcolor{red}{↦ Diagonal of the square = \sqrt{2 × Side} }}$

☬ HOPE IT HELPS YOU ☬