Question

Question :

• Length of a rectangle is 2 cm more than twice its breadth. If the perimeter of the rectangle is 34cm, find its length and breadth.


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Answer 1

Answer:

• The Length and breadth are 12cm and 5cm respectively

Step-by-step explanation:

Given:

• Length of a rectangle is 2 cm more than twice its breadth.
• If the perimeter of the rectangle is 34cm

To Find:

• find the length and breadth of the rectangle

Assumptions:

• Let the breadth of the rectangle be x
• Let the length of the rectangle be 2x + 2cm

Solution:

✰ As we know that,

• ${\pink{\star{\boxed{\frak{Perimeter = 2 ( L + B ) }}}}}$

✰ According to the question,

$\rightarrow \qquad \tt 34 = 2 ( 2x + 2 + x )$

$\rightarrow \qquad \tt 34= 2x + 4x + 4$

$\rightarrow \qquad \tt 34 = 6x + 4$

$\rightarrow \qquad \tt 6x = 34 - 4$

$\rightarrow \qquad \tt 6x = 30$

$\rightarrow \qquad \tt x = \cancel\dfrac{30}{6}$

$\rightarrow \qquad {\purple{\underline{\boxed{\frak{ x = 5 }}}\bigstar}}$

✰ Now let's find the dimensions,

$\nrightarrow \qquad \sf Length = 2x + 2 = 2( 5 ) + 2 = 12cm$

$\nrightarrow \qquad \sf Breadth = 1x = 1(5) = 5cm$

Verification:

$\rightarrow \qquad \tt 34 = 2 ( L + B )$

$\rightarrow \qquad \tt 34 = 2 ( 12 + 5 )$

$\rightarrow \qquad \tt 34 = 2 ( 17)$

$\rightarrow \qquad {\purple{\underline{\boxed{\frak{ 34 = 34 }}}\bigstar}}$

Therefore:

• The dimensions of the rectangle are 12cm and 5cm

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Answer 2

Solution:-

Given that:

• Length of a rectangle is 2 cm more than twice its breadth.
• The perimeter of the rectangle is 34 cm.

To find:-

• The length and breadth of the rectangle.

Required Formula:-

• Perimeter of rectangle = 2(l + b)

Step-by-step explanation:

• Let the breadth be x cm and length be 2x + 2 cm respectively.

Then,

$\\ :\implies\sf{34 = 2\bigg((2x+2) + x\bigg)}\\ \\ :\implies\sf{34=(4x+4)+2x}\\ \\ :\implies\sf{34 =6x+4}\\ \\ :\implies\sf{34-4=6x}\\ \\ :\implies\sf{30=6x}\\ \\ :\implies\sf{x=\frac{\cancel{30}}{\cancel{6}}}\\ \\ :\implies\underline{\boxed{\mathfrak{\blue{x=5}}}}\; \bigstar$

Therfore,

• breadth = x = 5 cm
• length = 2x + 2 = 2(5) + 2 = 10 + 2 = 12 cm

Hence,

• The length of rectangle is 12 cm and breadth of rectangle is 5 cm.

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