Certainly! Let's solve this step-by-step:
### Part (i): Finding the length and breadth of the garden
Since the area of a square is given by the formula:
[tex]\[ \text{Area} = \text{side} \times \text{side} \][/tex]
We can denote the side length of the square garden by [tex]\( s \)[/tex]. Given the area of the garden is 625 m²:
[tex]\[ s \times s = 625 \][/tex]
[tex]\[ s^2 = 625 \][/tex]
To find the side length, we take the square root of 625:
[tex]\[ s = \sqrt{625} \][/tex]
[tex]\[ s = 25 \text{ meters} \][/tex]
So, the length and breadth of the square garden are each 25 meters.
### Part (ii): Calculating the increase in area when the length and breadth are increased by 2 meters
If the length and the breadth of the garden are each increased by 2 meters, the new side length of the square garden will be:
[tex]\[ \text{New side length} = 25 + 2 = 27 \text{ meters} \][/tex]
Now, we find the new area of the garden with the increased side length:
[tex]\[ \text{New area} = 27 \times 27 = 729 \text{ m}^2 \][/tex]
Next, we need to determine the increase in area:
[tex]\[ \text{Increase in area} = \text{New area} - \text{Initial area} \][/tex]
[tex]\[ \text{Increase in area} = 729 - 625 \][/tex]
[tex]\[ \text{Increase in area} = 104 \text{ m}^2 \][/tex]
So, the area of the garden is increased by 104 square meters when the length and breadth are each increased by 2 meters.
