Question

8. The length of a rectangle is twice its breadth. If the ratio of the perimeter of the rectangle and its are
1:2, find the dimensions of the rectangle.
A fronti​

Answer 1

Answer:

Length= 12 units

Breadth = 6 units

Step-by-step explanation:

Let the breadth be x

then length will be 2x

According to the question,

Area : perimeter = 2 : 1

=> (l × b) : 2(l + b) = 2 : 1

=> (2x × x) : 2(2x + x) = 2 : 1

=> 2x² : 6x = 2 : 1

=> 2x²/6x = 2/1

=> 1/3x = 2

=> x = 2*3

=> x = 6unit

Hence,

breadth = x = 6units

length is 2x = 12units

Answer 2

☆ Solution ☆

Given

• The length of a rectangle is twice its breadth.
• If the ratio of the perimeter of the rectangle and its are 1 : 2.

To Find

• The dimensions of the rectangle.

Step-by-Step-Explaination

Let breadth of rectangle = x cm

Then, the length of the rectangle = 2x cm

Perimeter and area are given in the ratio 1 : 2

So,

perimeter : area = 1 : 2

$\frac{perimeter}{area}$ = $\frac{1}{2}$

As we know that :-

Perimeter of rectangle = 2 ( l + b )

Area of rectangle = l × b

So,

$\frac{2(l + b)}{ l \times b} = \frac{1}{2}$

By cross multiplication

2 { 2 ( l + b )} = 1 ( l × b )

put l = 2x

and b = x

2 { 2 ( 2x + x ) } = 1 ( 2x × x )

2 ( 6x ) = 1 × ${2x}^{2}$

12x = ${2x}^{2}$

${2x}^{2}$ = 12x

By transposition

${2x}^{2}$ - 12x = 0

2x ( x - 6 ) = 0

Therefore,

2x = 0 or x - 6 = 0

Then x = $\frac{0}{2}$ = 0

Or

x = 6

We got x now

Now find breadth

B = x = 6

And length = 2x = 2 × 6 = 12