The perimeter of a rectangular garden is 322 m. If the width of the garden is 72 m, what is its length? Length of the garden: m (b) The area of a rectangular window is 8342 cm². If the length of the window is 97 cm, what is its width? Width of the window: cm

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!

Solve problems involving the perimeter of a rectangular garden and the area of a rectangular window. Learn how to find the length of a garden with a perimeter of 322 m and width of 72 m, and the width of a window with an area of 8342 cm² and length of 97 cm. Suitable for students in Grades 6-8.

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