Question

the length of a rectangle is one centimetre more than its width and its perimeter is 14 cm, then the area of the rectangle is​

Answer 1

Answer:

let the width of rectangle be x

then it's length be (x+1)

perimeter of rectangle=14

2(l+b)=14

2(x+1+x)=14

2(2x+1)=14

2x+1=7

2x=6

x=3

breadth=x=3 cm

length=(x+1)=3+1=4 cm

area of rectangle=l×b=3×4

area of rectangle=12 cm^2

Answer 2

Answer :-

$\large{\underline{\boxed{\sf Area = 12 sq.cm}}}$

Explanation :-

Given :

• The length of rectangle is 1 cm more than it's breadth
• Perimeter of the rectangle - 14 cm

To find :

The area of the rectangle

Solution :

Let the breadth be 'x' cm

and the length be '(x + 1)' cm

We know that,

Perimeter = 2(length + breadth)

Perimeter = 14 cm

According to question,

$\sf\longrightarrow 2(x + x + 1) = 14$

$\sf\longrightarrow 2(2x + 1) = 14$

$\sf\longrightarrow 4x + 2 = 14$

$\sf\longrightarrow 4x = 14 - 2$

$\sf\longrightarrow 4x = 12$

$\sf\longrightarrow x = \dfrac{12}{4}$

$\sf\longrightarrow x = 3$

Therefore,

The breadth => x = 3 cm

The length => (x + 1) = 3 + 1 = 4 cm

Now,

$\large{\underline{\boxed{\sf Area = (length*breadth)}}}$

$= (4 \times 3) {cm}^{2}$

$= 12 \: {cm}^{2}$

Hence, the area of the rectangle is 12 cm² respectively