(a) To find the width of the rectangular field, we can use the formula for the perimeter of a rectangle, which is given by:
\[ P = 2 \times (L + W) \]
where \( P \) is the perimeter, \( L \) is the length, and \( W \) is the width.
Given:
- \( P = 314 \) m
- \( L = 98 \) m
We can rearrange the formula to solve for the width \( W \):
\[ 314 = 2 \times (98 + W) \]
Dividing both sides by 2:
\[ 157 = 98 + W \]
Now, subtract 98 from both sides:
\[ W = 157 - 98 = 59 \text{ m} \]
Width of the field: 59 m
(b) To find the length of the rectangular painting, we can use the formula for the area of a rectangle, which is:
\[ A = L \times W \]
where \( A \) is the area, \( L \) is the length, and \( W \) is the width.
Given:
- \( A = 4488 \) cm²
- \( W = 51 \) cm
We can rearrange the formula to solve for the length \( L \):
\[ 4488 = L \times 51 \]
Now, divide both sides by 51:
\[ L = \frac{4488}{51} \]
Calculating that:
\[ L = 88 \text{ cm} \]
Length of the painting: 88 cm
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