Question

the question of a rectangle board is double its breadth. the perimeter of the board is 24cm. find the dimension of the board. what is the area of the board​

Answer 1

Correct question :-

The length of a rectangle board is twice it's breadth. The perimeter of the board is 24 cm. Find the dimensions of the board. What is the area of the board?

$\sf\huge\underline{Answer}$

The dimensions of the rectangular board are 4 cm and 8 cm respectively. The area of the board is 32 cm²

Explanation :-

Given :

• Length = Twice the breadth
• Perimeter = 24 cm

To find :

The dimensions and area of the rectangular board

Solution :

Let the breadth be x

and the length be 2x

We know that,

Perimeter = 2 (length + breadth)

=> Perimeter = 24 cm

=> 2 (2x + x) = 24

=> 2 × 3x = 24

=> 6x = 24

=> x = 24/6

=> x = 4

Hence, the value of x is 4

Now,

The length of the rectangular board (x) = 4 cm

The breadth (2x) => 2 × 4 = 8 cm

We know that,

Area of rectangle = (Length × Breadth) sq. unit

= (4 × 8) cm²

= 32 cm²

Hence, the area of the rectangular board is 32 cm²

Answer 2

Answer:-

A = 32 cm²

Given :-

Length of rectangle is double to its breadth.

P = 24 cm

To find :-

Dimension of rectangular board.

Solution:-

Let the dimension of rectangular board be l and b respectively.

A/Q

$l = 2b$

Perimeter of rectangle is given by :-

$\huge \boxed {P = 2(l+b)}$

→$24 = 2(l + b)$

put the value of l.

→$24 = 2 ( 2b+b)$

→$24 = 2(3b)$

→$24 = 6b$

→$b = \dfrac{24}{6}$

→$\huge b = 4cm$

Now,

l = 2b

l = 2 × 4

l = 8 cm

Area of rectangle is given by :-

$\huge \boxed{A = l\times b}$

→$A = 8 \times 4$

→$\huge A = 32 cm^2$

hence,

The area of rectangle will be 32cm².