Question

The perimeter of a rectangle is 28 cm and its length is 2 cm more than double of its breadth x cm. Find the length of the rectangle.

Answer 1

Given,

• The Perimeter of a Rectangle is 28 cm.
• Its length is 2 cm more than double of its breadth x cm.

To Find,

• Length of Rectangle

Solution,

⇒Suppose the Breadth of Rectangle be a cm

So , Length of Rectangle be 2a + 2 cm

$\mapsto \underline{\sf{\pink{According \ to \ the \ Question :}}}$

$\implies \sf{Perimeter \ of \ Rectangle = 2(Length + Breadth)}$

$\implies \sf{Perimeter \ of \ Rectangle = 2(2a + 2 + a)}$

$\implies \sf{2(2a + 2 + a) = 28}$

$\implies \sf{2(3a + 2 ) = 28}$

$\implies \sf{6a + 4 = 28}$

$\implies \sf{6a = 28 - 4}$

$\implies \sf{6a = 24}$

$\implies \sf{a = \dfrac{24}{6}}$

$\implies \boxed{\sf{a = 4}}$

Now Put the Value of a in Length and find value :-

$\implies \sf{Length = 2a + 2}$

$\implies \sf{Length = 2(4) + 2}$

$\implies \sf{Length = 8 + 2}$

$\implies \boxed{\sf{Length = 10 \ cm}}$

Therefore,

$\boxed{\bold{\purple{Length of \ Rectangle = 2a + 2 = 8 + 2 = 10 \ cm}}}$

$\rule{200}2$

Answer 2

Given

Perimeter of rectangle = 28 cm

Length is 2 cm more than double of its breadth x.

To find

Length of rectangle

Solution

Here, given that the breadth is x cm.

⇰ Length of rectangle = 2x + 2

As we know that,

⟼ Perimeter of rectangle = 2(l + b)

Putting values :

➻ 28 = 2(2x + 2 + x)

➻ 28/2 = 3x + 2

➻ 14 = 3x + 2

➻ 14 - 2 = 3x

➻ 12 = 3x

➻ x = 12/3

➻ x = 4

Now finding length of rectangle :

➝ Length of rectangle = 2x + 2

➝ Length of rectangle = 2(4) + 2

➝ Length of rectangle = 8 + 2

➝ Length of rectangle = 10 cm

Therefore,

Length of rectangle = 10 cm.