Question

if the length of a rectangle is 3 meters more than the breadth, the perimeter of the rectangle is 22 find the length and breadth

Answer 1

Answer:

Step-by-step explanation

Let the breadth be x m.

Length = (x+3) m

Perimeter of rectangle= 22 m

2(l+b)=22

x+x+3=22÷2

2x+3=11

2x=11-3

x=8÷2

x=4.

Breadth= x m= 4 m

Length= (x+3)m

4+3 m

7m.

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Answer 2

Given :

• Length of the rectangle is 3 meters more than the breadth.
• Perimeter of the rectangle = 22

To find :

• The length and breadth of the rectangle.

Formula to be used :

$\sf\:Rectangle_{perimeter}$ = $\bf\:2(l+b)$

where, l denotes length and b denotes the breadth of the rectangle.

Assumption :

Let the breadth of the rectangle be x

Solution :

According to the question,

Length of the rectangle = 3 more than the breadth

Length of the rectangle = ( 3+x )

Again following the question,

$\sf\:Rectangle_{perimeter}~=~22~m$

Applying the above mentioned formula,

$\sf\dashrightarrow\:2(l+b)~=~22~$

$\sf\dashrightarrow\:2\left[(3+x)+x\right]~=~22~$

$\sf\dashrightarrow\:2\left[3+x+x\right]~=~22~$

$\sf\dashrightarrow\:2\left[3+2x\right]~=~22~$

$\sf\dashrightarrow\:6+4x~=~22~$

$\sf\dashrightarrow\:4x~=~16~$

$\sf\dashrightarrow\:x~=~\cancel{\frac{16}{4}}~$

$\sf\dashrightarrow$$\tt\red{x~=~4}$

Therefore,

Length of the rectangle = 3+x = 3 + 4 = 7m

Breadth of the rectangle = x = 4m

Verification :

$\sf\:Rectangle_{perimeter}~=~22~m$

$\sf\rightrightarrows\:2(l+b)~=~22~$

$\sf\rightrightarrows\:2(7+4)~=~22~$

$\sf\rightrightarrows\:2 \times 11~=~22~$

$\sf\rightrightarrows\:22~=~22~$

Hence Verified!~

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