Here is the extracted problem from the image:

"Diketahui suatu persegi panjang memiliki keliling 18 cm. Tentukan ukuran panjang, lebar, dan luas daerah persegi panjang yang mungkin."

Translation:

It is given that a rectangle has a perimeter of 18 cm. Determine the possible length, width, and area of the rectangle.

Solution:

The formula for the perimeter of a rectangle is: $P = 2 \times (p + l)$ where:

• $P$ = Perimeter
• $p$ = Length
• $l$ = Width

Since the perimeter is 18 cm: $18 = 2 \times (p + l)$ $p + l = \frac{18}{2} = 9$

Now, $p$ and $l$ are pairs of numbers that sum to 9. Let’s list some possibilities:

1. If $p = 1$, $l = 9 - 1 = 8$
2. If $p = 2$, $l = 9 - 2 = 7$
3. If $p = 3$, $l = 9 - 3 = 6$
4. If $p = 4$, $l = 9 - 4 = 5$

We can now compute the area for each possibility using the formula: $A = p \times l$

1. $p = 1, l = 8 \Rightarrow A = 1 \times 8 = 8 \, \text{cm}^2$
2. $p = 2, l = 7 \Rightarrow A = 2 \times 7 = 14 \, \text{cm}^2$
3. $p = 3, l = 6 \Rightarrow A = 3 \times 6 = 18 \, \text{cm}^2$
4. $p = 4, l = 5 \Rightarrow A = 4 \times 5 = 20 \, \text{cm}^2$

Answer:

Possible dimensions and their respective areas are:

1. $p = 1$ cm, $l = 8$ cm, $A = 8 \, \text{cm}^2$
2. $p = 2$ cm, $l = 7$ cm, $A = 14 \, \text{cm}^2$
3. $p = 3$ cm, $l = 6$ cm, $A = 18 \, \text{cm}^2$
4. $p = 4$ cm, $l = 5$ cm, $A = 20 \, \text{cm}^2$

Do you need further details or a specific explanation?

Related Questions:

1. How do you find the perimeter if only the area is known?
2. What happens if the rectangle becomes a square?
3. How does the relationship between perimeter and area change as dimensions vary?
4. Can two different rectangles have the same perimeter and area?
5. How would the solution change if the perimeter were a decimal number?

Tip:

The largest area for a given perimeter is achieved when the shape is a square.