Question

If the perimeter and breadth of a rectangle are 40cm and 9cm respectively. Find its length.​

Answer 1

Step-by-step explanation:

perimeter =40cm

breadth=9cm

length=?

2(l+b)=40

2(l+9)=40

l+9=40÷2

l+9=20

l=20-9

l=11

therefore length =11

Answer 2

Answer:

Diagram :

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large11 cm}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large9 cm}\put(-0.5,-0.4){\bf}\put(-0.5,3.2){\bf}\put(5.3,-0.4){\bf}\put(5.3,3.2){\bf}\end{picture}$

$\begin{gathered}\end{gathered}$

Given :

• Perimeter of Rectangle = 40 cm
• Breadth of Rectangle = 9 cm

$\begin{gathered}\end{gathered}$

To Find :

• Lenght of Rectangle

$\begin{gathered}\end{gathered}$

Concept :

★ Here the concept of Perimeter of Rectangle has been used. We are given that Perimeter of Rectangle is 40 cm and Breadth of Rectangle is 9 cm.We need to find the length of Rectangle.

★ So,We'll find the Lenght of Rectangle by insert the values in the required  formula.

$\begin{gathered}\end{gathered}$

Using Formula :

$\bigstar{\underline{\boxed{\bf{\red{Perimeter_{(Rectangle)} = 2(Length + Breadth)}}}}}$

$\begin{gathered}\end{gathered}$

Solution :

$\red\bigstar$ Here

• Perimeter of Rectangle = 40 cm
• Breadth of Rectangle = 9 cm

$\begin{gathered}\end{gathered}$

$\red\bigstar$ Finding the Lenght of Rectangle

${\dashrightarrow{\pmb{\sf{Perimeter \: of \: Rectangle = 2(Length + Breadth)}}}}$

• Substuting the values

${\dashrightarrow{\sf{40 \: cm= 2(Lenght+ 9)}}}$

${\dashrightarrow{\sf{\dfrac{40}{2} = (Lenght+ 9)}}}$

${\dashrightarrow{\sf{\cancel{\dfrac{40}{2}}= (Lenght+ 9)}}}$

${\dashrightarrow{\sf{20= (Lenght+ 9)}}}$

${\dashrightarrow{\sf{Lenght =20 - 9 }}}$

${\dashrightarrow{\sf{Lenght =11 \: cm }}}$

$\bigstar{\underline{\boxed{\bf{\purple{Lenght \: of \: rectangle = 11 \: cm }}}}}$

∴ The lenght of rectangle is 11 cm.

$\begin{gathered}\end{gathered}$

Verification :

$\red\bigstar$ Checking our answer

${\dashrightarrow{\pmb{\sf{Perimeter \: of \: Rectangle = 2(Length + Breadth)}}}}$

• Substuting the values

${\dashrightarrow{\sf{40= 2(11 + 9)}}}$

${\dashrightarrow{\sf{40= 2(20)}}}$

${\dashrightarrow{\sf{40= 2 \times 20}}}$

${\dashrightarrow{\sf{40 \: cm= 40 \: cm}}}$

$\bigstar{\underline{\boxed{\bf{\purple{LHS = RHS }}}}}$

∴ Hence Verified!

$\begin{gathered}\end{gathered}$

Learn More :

$\red\bigstar$ Formulas of area

$\boxed{\begin {minipage}{9cm}\\ \dag\quad \Large\underline{\bf Formulas\:of\:Areas:-}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Breadth\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}p\sqrt {4a^2-p^2}\\ \\ \star\sf Parallelogram =Breadth\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {minipage}}$

$\begin{gathered}\end{gathered}$

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