Question

the length of a rectangle is twice of its breadth . find the dimensons if the perimeter of the rectangle Is: (a) 156cm
and (b) 219 cm​

Answer 1

Answer a :-

• The dimensions of the rectangle are 26 cm and 52 cm.

Given :-

• The length of a rectangle is twice it's breadth.
• The perimeter of the rectangle is 156 m.

To find :-

• The dimensions of the rectangle.

Step-by-step explanation :-

We know that :-

Perimeter of a rectangle = 2 (L + B)

We will use this formula to find the answer.

Let the breadth of the rectangle be b.

Then the length will be 2b, since it's twice of the breadth.

Calculations :-

Now, let's apply the formula.

Substituting the given values,

$\tt2 \: (b + 2b) = 156$

Removing the brackets,

$\tt2b + 4b = 156$

Adding 2b and 4b,

$\tt6b = 156$

Transposing 6 from LHS to RHS, changing its sign,

$\tt b = \dfrac{156}{6}$

Dividing 156 by 6,

$\tt b = 26.$

The breadth = 26 cm.

So,

$\bf The \: length = 2b = 2 \times 26 = 52 \: cm$

Hence, the length = 52 cm and the breadth = 26 cm.

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Answer b :-

• The dimensions of the rectangle are 36.5 cm and 73 cm.

Given :-

• The length of a rectangle is twice it's breadth.
• The perimeter of the rectangle is 219 cm.

To find :-

• The dimensions of the rectangle.

Step-by-step explanation :-

We know that :-

Perimeter of a rectangle = 2 (L + B)

We will use this formula to find the answer.

Let the breadth of the rectangle be b.

Then the length will be 2b, since it's twice of the breadth.

Calculations :-

Now, let's apply the formula.

Substituting the given values,

$\tt2 \: (b + 2b) = 219$

Removing the brackets,

$\tt2b + 4b = 219$

Adding 2b and 4b,

$\tt6b = 219$

Transposing 6 from LHS to RHS, changing its sign,

$\tt b = \dfrac{219}{6}$

Dividing 219 by 6,

$\tt b = 36.5.$

The breadth = 36.5 cm.

So,

$\sf The \: length =2b = 2 \times 36.5 = 73 \: cm.$

Hence, the length = 73 cm and the breadth = 36.5 cm.

Answer 2

$\huge{\underline{\boxed{\sf{Answer 1 }}}}$

In the first case, perimeter of rectangle is given to be 156cm and we have to find dimensions of rectangle when length is twice of Breadth.

Let us assume breadth be x.

So length will become 2 x.

Now applying formula of perimeter of rectangle:

★Perimeter of rectangle=2(L+B)

$\Large{\boxed{\sf Here\left \{ {{L=Length} \atop {B=Breadth}} \right }}$

Now put values of perimeter, Length and breadth:

⇒ 156cm=2(2x+x)

⇒ 156cm=2(3x)

⇒ 156cm=6x

Divide by 6 both sides

⇒ 156÷6cm=6x÷6

⇒ 26cm=x

___________________________

Now,

Breadth of rectangle=x

Breadth of rectangle=26cm

Length of rectangle=2x

Length of rectangle=2×26cm

Length of rectangle=52cm

So the required dimensions are 52cm and 26cm.

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$\underline{\huge{\boxed{\sf{Answer\: 2 }}}}$

In the 2nd case we are given perimeter to be 219cm and we have to find dimensions of rectangle when length is 2 times of breadth.

Let us assume breath be y

So length will be 2y

Now applying formula for perimeter of rectangle:

Perimeter of rectangle=2(L+B)

$\Large {\boxed{\sf Here\left \{ {L=Length} \atop {B=Breadth}} \right.}}$

Now putting values of perimeter, length and breadth:

⇒ 219cm=2(2y+y)

⇒ 219cm=2(3y)

⇒ 219cm=6y

Divide by 6 both sides

⇒ 219cm ÷6=6y÷6

⇒ 36.5cm=y

___________________________

Now,

Breadth of rectangle=y

Breadth of rectangle=36.5cm

Length of rectangle=2y

Length of rectangle=2×36.5cm

Length of rectangle=73cm

So the required dimensions of rectangle are 36.5cm and 73cm.

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