Question

the perimeter of a rectangle is 40m if it's length is 12th find its breadth also find its area​

Answer 1

Answer :-

• The breadth of the rectangle = 8 m.
• The area of the rectangle = 96 m².

Given :-

• The perimeter of the rectangle = 40 m.
• It's length = 12 m.

To find :-

• It's breadth.
• It's area.

Step-by-step explanation :-

• In this question, it has been given that the perimeter of a rectangle is 40 m and it's length is 12 m. We have to find it's breadth and area. For this, we are first going to find the breadth of the rectangle using the formula required for finding the perimeter of a rectangle. Then we are going to find it's area by using the formula required for this purpose.

Calculations :-

We know that :-

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

Here,

• Perimeter = 40 m.
• Length = 12 m.

• Let the breadth be b.

Now, let's apply this formula.

$\tt \implies 40 = 2 \: (12 + b)$

Removing the brackets,

$\implies \tt40 = 24 + 2b$

Transposing 24 from RHS to LHS, changing it's sign,

$\implies \tt40 - 24 = 2b$

Subtracting the numbers,

$\tt \implies 16 = 2b$

Transposing 2 from RHS to LHS, changing it's sign,

$\tt \implies \dfrac{16}{2} = b$

Dividing 16 by 2,

$\underline{\boxed{\tt\implies 8 = b.}}$

• The breadth of the rectangle = 8 m.

• Now, let's find the area of the rectangle using it's length and breadth.

We know that :-

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

Here,

• Length = 12 m.
• Breadth = 8 m.

So let's apply this formula.

$\bf\implies Area = 12 \times 8$

Multiplying the numbers,

$\underline{\boxed{\bf\implies Area = 96.}}$

• The area of the rectangle = 96 m².