Finding Length or Width of a Rectangle from Area Worksheets - Free Printable

To solve the problems in the worksheet, we need to use the formula for the area of a rectangle:

\[
\text{Area} = \text{Length} \times \text{Width}
\]

We will rearrange this formula as needed to find either the length or the width based on the given information.

---

Problem 1:

- Given: Area = 70 ft², Width = 7 ft
- Find: Length

Using the formula:
\[
\text{Length} = \frac{\text{Area}}{\text{Width}}
\]
\[
\text{Length} = \frac{70}{7} = 10 \text{ ft}
\]

Answer: Length = 10 ft

---

Problem 2:

- Given: Area = 96 yd², Width = 8 yd
- Find: Length

Using the formula:
\[
\text{Length} = \frac{\text{Area}}{\text{Width}}
\]
\[
\text{Length} = \frac{96}{8} = 12 \text{ yd}
\]

Answer: Length = 12 yd

---

Problem 3:

- Given: Area = 105 in², Length = 15 in
- Find: Width

Using the formula:
\[
\text{Width} = \frac{\text{Area}}{\text{Length}}
\]
\[
\text{Width} = \frac{105}{15} = 7 \text{ in}
\]

Answer: Width = 7 in

---

Problem 4:

- Given: Area = 65 in², Length = 13 in
- Find: Width

Using the formula:
\[
\text{Width} = \frac{\text{Area}}{\text{Length}}
\]
\[
\text{Width} = \frac{65}{13} = 5 \text{ in}
\]

Answer: Width = 5 in

---

Problem 5:

- Given: Area = 48 ft², Width = 4 ft
- Find: Length

Using the formula:
\[
\text{Length} = \frac{\text{Area}}{\text{Width}}
\]
\[
\text{Length} = \frac{48}{4} = 12 \text{ ft}
\]

Answer: Length = 12 ft

---

Problem 6:

- Given: Area = 176 yd², Width = 11 yd
- Find: Length

Using the formula:
\[
\text{Length} = \frac{\text{Area}}{\text{Width}}
\]
\[
\text{Length} = \frac{176}{11} = 16 \text{ yd}
\]

Answer: Length = 16 yd

---

Problem 7:

- Given: Area = 112 yd², Length = 16 yd
- Find: Width

Using the formula:
\[
\text{Width} = \frac{\text{Area}}{\text{Length}}
\]
\[
\text{Width} = \frac{112}{16} = 7 \text{ yd}
\]

Answer: Width = 7 yd

---

Problem 8:

- Given: Area = 18 in², Length = 9 in
- Find: Width

Using the formula:
\[
\text{Width} = \frac{\text{Area}}{\text{Length}}
\]
\[
\text{Width} = \frac{18}{9} = 2 \text{ in}
\]

Answer: Width = 2 in

---

Problem 9:

- Given: Area = 33 ft², Width = 3 ft
- Find: Length

Using the formula:
\[
\text{Length} = \frac{\text{Area}}{\text{Width}}
\]
\[
\text{Length} = \frac{33}{3} = 11 \text{ ft}
\]

Answer: Length = 11 ft

---

Final Answers:

1. Length = 10 ft
2. Length = 12 yd
3. Width = 7 in
4. Width = 5 in
5. Length = 12 ft
6. Length = 16 yd
7. Width = 7 yd
8. Width = 2 in
9. Length = 11 ft

\boxed{
\begin{array}{ccc}
1) & \text{Length} = 10 \text{ ft} & \\
2) & \text{Length} = 12 \text{ yd} & \\
3) & \text{Width} = 7 \text{ in} & \\
4) & \text{Width} = 5 \text{ in} & \\
5) & \text{Length} = 12 \text{ ft} & \\
6) & \text{Length} = 16 \text{ yd} & \\
7) & \text{Width} = 7 \text{ yd} & \\
8) & \text{Width} = 2 \text{ in} & \\
9) & \text{Length} = 11 \text{ ft} & \\
\end{array}
}