Question

the lenght of a rectangle is 1 cm more than 2 times its breadth . Its perimeter is 62 cm. what is its lenght

Answer 1

Given :

the lenght of a rectangle is 1 cm more than 2 times its breadth . Its perimeter is 62 cm.

To find :

it's length

Solution:

Let the breadth of the rectangle be x cm.

Then the length of the rectangle will be (2x +1)cm.

➸ 2 x length + 2 x breadth = perimeter of rectangle

➸ 2 (2x + 1)+ 2x - 62

➸ 4x +2 + 2x = 62

➸ 6x + 2 = 62

➸ 6x = 62 - 2 = 60

➸ x = 60/6

➸ x = 10

➸ Breadth of rectangle is 10 cm.

➸ Length of the rectangle = 2x +1

➸ 2 x 10 + 1

∴ Length of rectangle = 21 cm.

Answer 2

Answer:

Let the Breadth be x and Length be (2x + 1)

$\setlength{\unitlength}{1.5cm}\begin{picture}(8,2)\linethickness{0.4mm}\put(7.7,3){\large\sf{A}}\put(7.7,2){\sf{\large{x}}}\put(7.7,1){\large\sf{B}}\put(9,0.7){\sf{\large{(2x + 1)}}}\put(11.1,1){\large\sf{C}}\put(11.1,3){\large\sf{D}}\put(8,1){\line(1,0){3}}\put(8,1){\line(0,2){2}}\put(11,1){\line(0,3){2}}\put(8,3){\line(3,0){3}}\end{picture}$

$\underline{\bigstar\:\textsf{According to the given Question :}}$

$:\implies\sf Perimeter = 2(Length+Breadth)\\\\\\:\implies\sf 62 = 2\bigg\lgroup(2x+1)+x\bigg\rgroup\\\\\\:\implies\sf62 = 2 \times (3x + 1)\\\\\\:\implies\sf31 = 3x + 1\\\\\\:\implies\sf31 - 1 = 3x\\\\\\:\implies\sf30 = 3x\\\\\\:\implies\sf x = 10$

$\rule{150}{1.5}$

$\bullet\:\:\textsf{Length = 2x + 1 = 2(10) + 1 = \textbf{21 cm}}\\\bullet\:\:\textsf{Breadth = x = \textbf{10 cm}}$