Question

The length and the breadth of a rectangle are in the ratio of 3: 2. Find its sides, if its perimeter is 2,500 cm.​

Answer 1

Given : The length and the breadth of a rectangle are in the ratio of 3 : 2.

To Find : Find length and breadth of rectangle ?

_________________________

Solution : Let the length of rectangle (L) 3y & breadth of rectangle (B) 2y

$~$

$\underline{\frak{\pmb{As~we~know~that~:}}}$

• Perimeter of rectangle = 2(L + B)

$~$

$\underline{\frak{\pmb{According ~to ~the ~question~:}}}$

➻ 2500 = 2(3y + 2y)

➻ 2500 = 2(5y)

➻ 2500 = 2 × 5y

➻ 2500 = 10y

➻ 10y = 2500

➻ y = 2500/10

➻ y = 250/1

➻ y = 250

$~$

• Length of rectangle = 3(250)
• Length of rectangle = 3 × 250
• Length of rectangle = 750 cm

• Breadth of rectangle = 2(250)
• Breadth of rectangle = 2 × 250
• Breadth of rectangle = 500 cm

$~$

Hence,

• Length and Breadth of rectangle are 750 cm and 500 cm.

Answer 2

Answer:

Diagram :

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

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

Given :

• The length and the breadth of a rectangle are in the ratio of 3:2.
• The perimeter of rectangle is 2500 cm.

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

To Find :

• Side of rectangle

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

Using Formula :

$\small{\longrightarrow{\underline{\boxed{\pmb{\sf{Perimeter \: of \: rectangle = 2(l + b)}}}}}}$

☼ Where :-

• l = length
• b = breadth

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

Solution

☼ Here we have given that lenght and breadth of a rectangle are in the ratio of 3:2. So let the sides be :-

• Length = 3x
• Breadth = 2x

$\rule{300}{1.5}$

☼ Now, According to the question :-

${\longrightarrow{\sf{Perimeter \: of \: rectangle = 2(l + b)}}}$

${\longrightarrow{\sf{2500 \: cm = 2(3x + 2x)}}}$

${\longrightarrow{\sf{2500 \: cm = 2(5x)}}}$

${\longrightarrow{\sf{5x = \dfrac{2500}{2}}}}$

${\longrightarrow{\sf{5x = \cancel{\dfrac{2500}{2}}}}}$

${\longrightarrow{\sf{5x =1250}}}$

${\longrightarrow{\sf{x = \dfrac{1250}{5}}}}$

${\longrightarrow{\sf{x = \cancel{\dfrac{1250}{5}}}}}$

${\longrightarrow{\underline{\underline{\sf{x = 250 \: cm}}}}}$

${\bigstar{\underline{\boxed{\sf{\pink{x = 250 \: cm}}}}}}$

$\rule{300}{1.5}$

☼ Hence :-

• Lenght = 3x
• Lenght = 3 × 250 cm
• Lenght = 750 cm

∴ The lenght of rectangle is 750 cm.

• Breadth = 2x
• Breadth = 2 × 250 cm
• Breadth = 500 cm

∴ The breadth of rectangle is 500 cm.

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

Verification

${\longrightarrow{\sf{Perimeter \: of \: rectangle = 2(l + b)}}}$

${\longrightarrow{\sf{2500 \: cm= 2(750 + 500) \: cm}}}$

${\longrightarrow{\sf{2500 \: cm= 2(1250) \: cm}}}$

${\longrightarrow{\sf{2500 \: cm= 2 \times 1250 \: cm}}}$

${\longrightarrow{\sf{2500 \: cm= 2500 \: cm}}}$

${\longrightarrow{\underline{\underline{\sf{LHS = RHS}}}}}$

${\bigstar{\underline{\boxed{\sf{\pink{Hence \: Verified!}}}}}}$

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

Learn More :

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

$\rule{300}{1.5}$