An expression for the length of the rectangle in terms of the width would be Response area

Question

The formula for the area of a rectangle is Response area

Using trial and error, if the area is 96 m^2, then the length and width are

Answer 1

To derive an expression for the length of a rectangle in terms of the width, we start with the formula for the area of a rectangle:

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

Given that the area is 96 m², we can write:

$$96=\text{Length}\times \text{Width}$$

To express the length in terms of the width (let's denote the width as $W$), we can rearrange this formula:

$$\text{Length}=\frac{96}{W}$$

Now, using trial and error to find possible pairs of length and width that yield an area of 96 m², we can try different widths:

1. If $W=8$ m: $$\text{Length}=\frac{96}{8}=12\text{ m}$$

2. If $W=12$ m: $$\text{Length}=\frac{96}{12}=8\text{ m}$$

3. If $W=6$ m: $$\text{Length}=\frac{96}{6}=16\text{ m}$$

4. If $W=4$ m: $$\text{Length}=\frac{96}{4}=24\text{ m}$$

5. If $W=3$ m: $$\text{Length}=\frac{96}{3}=32\text{ m}$$

6. If $W=2$ m: $$\text{Length}=\frac{96}{2}=48\text{ m}$$

From these calculations, we find the following pairs of length and width that yield an area of 96 m²:

• Width = 8 m, Length = 12 m
• Width = 12 m, Length = 8 m
• Width = 6 m, Length = 16 m
• Width = 4 m, Length = 24 m
• Width = 3 m, Length = 32 m
• Width = 2 m, Length = 48 m

These are all the combinations of length and width for the rectangle with an area of 96 m².