Question 3

Let's find the area of the rectangle using the given length and different breadths.

Step 1 — Calculate Area for Breadth = 12 cm

We know the length is 13 cm.

The breadth is 12 cm.

The area of a rectangle is length multiplied by breadth.

$\text{Area} = \text{Length} \times \text{Breadth}$

$= 13 \times 12$

$\boxed{156 \text{ cm}^2}$

Step 2 — Calculate Area for Breadth = 10 cm

The length remains 13 cm.

The breadth is now 10 cm.

Let's use the area formula again.

$\text{Area} = \text{Length} \times \text{Breadth}$

$= 13 \times 10$

$\boxed{130 \text{ cm}^2}$

Step 3 — Calculate Area for Breadth = 8 cm

The length is still 13 cm.

The breadth is 8 cm.

We will apply the area formula one more time.

$\text{Area} = \text{Length} \times \text{Breadth}$

$= 13 \times 8$

$\boxed{104 \text{ cm}^2}$

Step 4 — Find the Linear Pattern

Let's represent the breadth as a variable.

Let the breadth be $x$ cm.

The length of the rectangle is fixed at 13 cm.

The area (A) is length multiplied by breadth.

$A = 13 \times x$

$\boxed{A = 13x}$

Answer

(i) The area is $156 \text{ cm}^2$. (ii) The area is $130 \text{ cm}^2$. (iii) The area is $104 \text{ cm}^2$. The linear pattern representing the area is $A = 13x$.