Question

The length of a rectangle is 3 cm more than twice the breadth.

If its perimeter is 72 cm, find the length and breadth.

Answer 1

Answer:

Step-by-step explanation:

ANSWER:

Let the Breadth = x

So, Length = 3+2x

Perimeter = 72 cm.

We need to find Length and Breadth.

We know the formula,

Perimeter = 2*(L +B)

Where ; L is length and B is breadth.

We are already given the perimeter.

So placing the assumption(s) and value:-

72 = 2(3+x+x)

72 = 2* (3+2x+x)

72 = 6 + 6x ___________________( Multiplying 2 in distributive property)

72-6 = 6x

6x = 66

x = 11 cm

Therefore , Breadth of the rectangle is 11 cm.

Now length is 3+2x

= 3+ 2(11)

= 3 +22

= 25cm is the Length of the Rectangle.

You may like to refer to attachment for the diagram.

Answer 2

Answer:

⋆ DIAGRAM :

$\setlength{\unitlength}{1.5cm}\begin{picture}(8,2)\linethickness{0.5mm}\put(7.7,3){\large\sf{A}}\put(7.3,2){\sf{\large{n cm}}}\put(7.7,1){\large\sf{B}}\put(9,0.7){\sf{\large{2n + 3 cm}}}\put(11.1,1){\large\sf{C}}\put(11.1,3){\large\sf{D}}\put(8,1){\line(1,0){3}}\put(8,1){\line(0,2){2}}\put(11,1){\line(0,3){2}}\put(8,3){\line(3,0){3}}\end{picture}$

$\rule{120}{1}$

Let the Breadth be n and Length be 2n + 3 of rectangle respectively.

$\underline{\bigstar\:\boldsymbol{According\:to\:the\:Question :}}$

$\dashrightarrow\sf\:\: Perimeter_{(Rectangle)}=2\bigg\lgroup Length+Breadth\bigg\rgroup\\\\\\\dashrightarrow\sf\:\:72=2\bigg\lgroup(2n+3)+n\bigg\rgroup\\\\\\\dashrightarrow\sf\:\:36 =2n +3 + n\\\\\\\dashrightarrow\sf\:\:36 - 3 = 2n +n\\\\\\\dashrightarrow\sf\:\:33 = 3n\\\\\\\dashrightarrow\sf\:\:\dfrac{33}{3} = n\\\\\\\dashrightarrow\sf\:\:n = 11$

$\rule{160}{2}$

$\underline{\bigstar\:\boldsymbol{Dimensions\:of\:the\: Rectangle :}}$

$\bullet\:\:\textsf{Length = 2n + 3 = 2(11) + 3 = \textbf{25 cm}}\\\bullet\:\:\textsf{Breadth = n =\textbf{11 cm}}$

⠀

$\therefore$ Length and Breadth are 25 cm and 11 cm of the rectangle respectively.