Question

a square of side 9cm has the same perimeter as a rectangle with length 11cm find the breadth and area of the rectangle​

Answer 1

Answer:

breadth of the rectangle: 7 cm

area of the rectangle: 36 cm

Answer 2

Answer:

• Breadth of the rectangle is 7 cm.
• Area of the rectangle is 77 cm².

Step-by-step explanation:

Given that:

• A square of side 9 cm has the same perimeter as a rectangle with length 11 cm.

To Find:

• Breadth and Area of the rectangle.

Solution:

As we know that:

• Perimeter of square = (4 × side) units

Substituting the values,

Perimeter = (4 × 9) cm

= 36 cm

As,

• It is mentioned that the perimeter of the square is equal to the perimeter of the rectangle.

Hence,

• Perimeter of the rectangle = 36 cm

As we know that:

• Perimeter of rectangle = 2(length + breadth) units

Let us assume:

• The breadth of the rectangle be b.

Substituting the values,

$\sf{\longmapsto36=2(11+b)}$

Opening the bracket,

$\sf{\longmapsto36=22+2b}$

Transposing 22 from RHS to LHS and changing its sign,

$\sf{\longmapsto36-22=2b}$

Subtracting LHS,

$\sf{\longmapsto14=2b}$

Transposing 2 from RHS to LHS and changing its sign,

$\sf{\longmapsto\dfrac{14}{2}=b}$

Dividing LHS,

$\sf{\longmapsto7=b}$

Hence,

• Breadth of the rectangle is 7 cm.

Now,

• Length of the rectangle = 11 cm
• Breadth of the rectangle = 7 cm

As we know that:

• Area of rectangle = (length × breadth) sq. units

Substituting the values,

Area of the rectangle = (11 × 7) cm²

= 77 cm²

Hence,

• Area of the rectangle is 77 cm².