Let's solve these two problems step by step.

(a) Finding the length of the garden:

We are given:

• The perimeter of the rectangular garden = 322 m
• The width of the garden = 72 m

The formula for the perimeter $P$ of a rectangle is:

$P = 2 \times (\text{length} + \text{width})$

Substitute the given values into the formula:

$322 = 2 \times (\text{length} + 72)$

Now, solve for the length: $322 = 2 \times (\text{length} + 72)$ $161 = \text{length} + 72$ $\text{length} = 161 - 72 = 89 \, \text{m}$

So, the length of the garden is 89 m.

(b) Finding the width of the window:

We are given:

• The area of the rectangular window = 8342 cm²
• The length of the window = 97 cm

The formula for the area $A$ of a rectangle is:

$A = \text{length} \times \text{width}$

Substitute the given values into the formula:

$8342 = 97 \times \text{width}$

Solve for the width: $\text{width} = \frac{8342}{97} = 86 \, \text{cm}$

So, the width of the window is 86 cm.

Final Answers:

1. Length of the garden: 89 m
2. Width of the window: 86 cm

Would you like further details or have any questions? Here are some related questions for practice:

1. What would be the area of the garden based on its dimensions?
2. If the perimeter of a rectangular park is 400 m and its width is 100 m, what is the length of the park?
3. If the area of a square window is 2500 cm², what is its side length?
4. How would the perimeter of the garden change if the width were reduced by 10 m?
5. If the area of a window is 6000 cm² and the width is 75 cm, what is the length?

Tip: When solving for length or width, remember that both the perimeter and area formulas for rectangles rely on knowing both dimensions, so isolating one variable makes solving easy!