Question

The perimeter of a rectangle is equal to that of square with with 13cm if the rectangle is 16cm long what it its breath

Answer 1

Appropriate Question :

The perimeter of a rectangle is equal to that of square with side 13 cm. If the rectangle is 16cm long what it its breadth.

Given

• Perimeter of rectangle = Perimeter of the square
• Side of the square = 13 cm
• Length of the rectangle = 16 cm

To find

• Breadth of the rectangle

Solution

Using formula,

Perimeter of square = 4 × side

Substituting the given values,

⟼ Perimeter = 4 × 13

⟼ Perimeter = 52

Perimeter of the square = 52 cm²

Perimeter of square = Perimeter of rectangle (given)

So, Perimeter of rectangle = 52 cm²

Using formula,

Perimeter of rectangle = 2(l + b)

where,

• l = length of the rectangle
• b = breadth of the rectangle

Substituting the given values,

⟼ 52 = 2(16 + b)

⟼ 52/2 = 16 + b

⟼ 26 = 16 + b

⟼ 26 - 16 = b

⟼ 10 = b

Breadth of the rectangle = 10 cm.

_________________________

Let's verify :-

Substitute the value of b in 52 = 2(16 + b)

Taking RHS,

⟼ 2(16 + 10)

⟼ 2(26)

⟼ 52

Lhs = Rhs

Hence, verified.

Answer 2

Correct Question :

The perimeter of a rectangle is equal to the perimeter of a square with side 13 cm . If the rectangle is 16 cm long . What is its breadth ?

Answer :

$\sf\pink{Given:}$

• perimeter of rectangle = perimeter of square .

• Side of square is 13 cm .

• length of the rectangle is 16 cm .

$\sf\pink{To\:find:}$

• Breadth of the rectangle ?

Explanation :

We can find breadth using the formula perimeter of rectangle is 2(l + b) . To find the perimeter of rectangle we need to find the perimeter of square because they both are equal .

Perimeter of square = 4 × side

$\longrightarrow\sf{ 4\times 13}$

$\longrightarrow\sf{ 52}$

• Therefore the perimeter of square is 52 cm .

• Perimeter of rectangle is therefore 52 cm too .

Perimeter of rectangle = 2( l + b )

$\longrightarrow\sf{ 52 = 2\times ( 16 + b)}$

$\longrightarrow\sf{ 52 = 36 + 2b}$

$\longrightarrow\sf{ 2b = 52 - 36}$

$\longrightarrow\sf{ 2b = 16}$

$\longrightarrow\sf{ b = \dfrac{16}{2}}$

$\longrightarrow\sf{ b = 8}$

• Therefore breadth of the rectangle is 8 cm.