Question

•The perimeter of a rectangle is 84cm
a) find the sum of their length and breadth?
b)if length is 12cm find its breadth and area?​

Answer 1

Step-by-step explanation:

(i). perimeter of rectangle = 2(length+breadth)

84 = 2( length+ breadth)

42 = length+breadth

so, sum of length and breadth is 42

(ii). we know that,

length + breadth = 42

12+ breadth =42

breadth = 30

so, breadth is 30 cm

Answer 2

Answer a :-

• The sum of length and breadth of the rectangle is 42 cm.  

To find :-

• The sum of the length and breadth of the rectangle.

Step-by-step explanation :-

• Here, it is given that the perimeter of a rectangle is 84 cm. We have to find the sum of it's length and breadth.  

We know that :-

$\underline{\boxed{\sf{Perimeter \: of \: a \: rectangle = 2 ( L + B)}}}$

Where,

• L = Length.
• B = Breadth.

Here,

• Perimeter = 84 cm.

Therefore :-

$\bf{\longrightarrow \: 2\: (L + B) = 84}$

$\bf{\longrightarrow \: (L + B) = \cancel{ \dfrac{84}{2}}}$

$\bf{\longrightarrow \: (L + B) = 42 \: cm}$

Hence,

• The sum of the length and breadth of the rectangle is 42 cm.

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Answer b :-

• The breadth of the rectangle is 30 cm.
• The area of the rectangle is 360 cm².

To find :-

• The breadth and area of the rectangle if it's length is 12 cm.

Step-by-step explanation :-

• Here, it is given that the perimeter of a rectangle is 84 cm. We have to find it's breadth and area. Let's find it's breadth first!

We know that :-

$\underline{\boxed{\sf{Perimeter \: of \: a \: rectangle = 2 \:( L + B)}}}$

Here,

• Perimeter = 84 cm.
• Length = 12 cm.

Let :-

• The breadth be "b" cm.

Therefore,

$\tt{\longrightarrow \: 2 (12 + b) = 84}$

$\tt{\longrightarrow \: (12 + b) =\cancel{\dfrac{84}{2}}}$

$\tt{\longrightarrow \: (12 + b) = 42}$

$\tt{\longrightarrow \: b = 42 - 12}$

$\tt{\longrightarrow \: b = 30 \: cm}$

Hence,

• The breadth of the rectangle is 32 cm.

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Now, we know that :-

$\underline{\boxed{\sf Area \: of \: a \: rectangle = L \times B}}$

Where,

• L = Length.
• B = Breadth.

Here,

• Length = 12 cm.
• Breadth = 30 cm.

Therefore,

$\dashrightarrow \rm Area = 12 \times 30$

$\rm \dashrightarrow Area = 360 \: cm^2$

 

Hence :-

• The area of the rectangle is 360 cm².

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