Question

The length of a rectangle is 2 less than 4 times the width . if the perimeter is 246 cm,find the length and the width of the rectangle

Answer 1

Answer:

The Length is 98 cm and Breadth is 25 cm.

Step-by-step explanation:

Gívєn -

Length of the Rectangle = 2 less than 4 times the Width

The Perimeter = 246 cm

Tσ fínd -

The Length and Width of the Rectangle

Sσlutíσn -

Let the -

• Breadth (Width) be as x
• Length be as (4x - 2)

★ Perimeter = $\boxed{\sf{2(Length+Breadth)}}$

$\sf{\implies} \: 246 = 2(4x - 2 + x)$

$\sf{\implies} \: 246 = 8x - 4 + 2x$

$\sf{\implies} \: 246 = 10x - 4$

$\sf{\implies} \: 246 + 4 = 10x$

$\sf{\implies} \: 10x = 250$

$\sf{\implies} \: x = \dfrac{250}{10}$

$\sf{\implies} \: x = 25$

Breadth (Width) = 25 cm

$\rule{300}{1.5}$

Length =

$\sf{\implies} \: 4x - 2 \\\sf{\implies}\: 4(25) - 2 \\ \sf{\implies} \:100 - 2 \\ \sf{\implies} \:98$

Length = 98

$\therefore$ The Length is 98 cm and Breadth is 25 cm.

$\rule{300}{1.5}$

Verification:

Place values of length and width, & check whether the Perimeter is 246 cm or not.

$\sf{\implies} \:2(98+25)=246$

$\sf{\implies} \:196+50=246$

$\sf{\implies} \:246=246$

$\therefore$ The Length is 98 cm and Breadth is 25 cm.

Answer 2

$\large{\mathfrak{\underline{\underline{Answer:-}}}}$

length = 98 cm

breadth = 25 cm

${\mathfrak{\underline{\underline{Step-By-Step-Explanation:-}}}}$

Given:-

Perimeter = 246 cm

________________________

To find :-

length and width

________________________

Solution :-

The length of the Rectangle is 2 less than 4 times its width.

» let breadth = x

So,

» Length = 4x - 2

Formula :-

$\large{\sf{\star{\boxed{\boxed{Perimeter \: = \: 2(length \: + \: breadth)}}}}}$

_________________[Put Values]

⇒ 246 = 2(4x - 2 + x)

⇒ 2(4x -2 + x) = 246

⇒ 2(5x - 2) = 246

⇒ 10x - 4 = 246

⇒ 10x = 246 +4

⇒ 10x = 250

⇒ x = 250/10

⇒ x = 25 ............(1)

Breadth (x) is 25 cm

________________________

Substitute value of (1) in length

length = 4 * 25 -2

⇒ length = 100 - 2

⇒length = 98

Length is 98 cm

___________________________

$\large{\mathfrak{\underline{\underline{Proof:-}}}}$

Perimeter = 2(length + Breadth)

246 = 2 (98 + 25)

246 = 2(123)

246 = 246