Question

The perimeter of rectangle is 40cm. The length of the rectangle is more than double it's breadth by 2. find the length and breadth.​

Answer 1

⇒ Given:

The perimeter of a rectangle is 40 cm.

The length of the rectangle is more than double of its breadth by 2 cm.

⇒ To Find:

The dimensions of the rectangle.

⇒ Solution:

In order to find the answer to this question, we need to form an algebraic equation out of the statements derived from the question. We will also have to use the perimeter formula to solve this question.

$\mathtt{\star\:Statement\:1}$

The perimeter of a rectangle is 40 cm.

$\mathtt{\star\:Statement\:2}$

The length of the rectangle is more than double of its breadth by 2 cm.

$\mathtt{\star\:Formula}$

Perimeter of a rectangle = 2 (l + b)

$\mathtt{\star\:Forming\:an\:algebraic\:expression}$

Let's assume that the measure of the breadth of the rectangle as "x". This means that the length of the rectangle is 2x + 2. Now, when we combine the given statements and formula, we can form an algebraic equation as shown below:

$\sf{\longrightarrow\:2(2x+2+x)=40\:cm}$

$\sf{\longrightarrow\:2(3x+2)=40\:cm}$

$\sf{\longrightarrow\:6x+4=40\:cm}$

$\sf{\longrightarrow\:6x=40-4}$

$\sf{\longrightarrow\:6x=36}$

$\sf{\longrightarrow\:x=\dfrac{36}{6}}$

$\sf{\longrightarrow\:x=6}$

Therefore:

✳ Breadth = x = 6 cm

✳ Length = 2x + 2 = 14 cm

The length and breadth of the rectangle are 6 and 14 cm respectively.

⇒ Verification:

It is given that the perimeter of the rectangle is 40 cm. If we apply the values into the perimeter formula and get the desired result, our answer is correct.

LHS:

= 2 (l + b)

= 2 (14 + 6)

= 2 x 20

= 40 cm

RHS:

40 cm

LHS = RHS

Hence verified!

Answer 2

Step-by-step explanation:

2(l+b)=40

1-2b=2

So l=2b +2....…………..(1)

So 2(2b+2+b)=40

2(3b+2)=40

3b+2=20

So b=6cm

And length 1 =14cm (from (1)) Hope it helps u dood..