Questions: How many feet of fencing should be purchased to enclose a rectangular garden that is 18 ft long and 14 ft wide? The wood framing for an art canvas costs 4.86 per foot. How much would the wood framing cost for a rectangular picture that measures 3 ft by 7 ft ?

Solution Steps

1. To find the amount of fencing needed to enclose a rectangular garden, calculate the perimeter of the rectangle. The perimeter \( P \) of a rectangle is given by the formula \( P = 2 \times (length + width) \).
2. To find the cost of wood framing for a rectangular picture, first calculate the perimeter of the rectangle using the same formula as above. Then, multiply the perimeter by the cost per foot of the wood framing.

The perimeter \( P \) of a rectangle is given by: \[ P = 2 \times (\text{length} + \text{width}) \]

For the garden: \[ \text{length} = 18 \, \text{ft} \] \[ \text{width} = 14 \, \text{ft} \]

Thus, \[ P = 2 \times (18 + 14) = 2 \times 32 = 64 \, \text{ft} \]

The perimeter \( P \) of a rectangle is given by: \[ P = 2 \times (\text{length} + \text{width}) \]

For the picture frame: \[ \text{length} = 3 \, \text{ft} \] \[ \text{width} = 7 \, \text{ft} \]

Thus, \[ P = 2 \times (3 + 7) = 2 \times 10 = 20 \, \text{ft} \]

The cost of the wood framing is given by: \[ \text{Total Cost} = \text{Perimeter} \times \text{Cost per Foot} \]

For the picture frame: \[ \text{Perimeter} = 20 \, \text{ft} \] \[ \text{Cost per Foot} = \$4.86 \]

Thus, \[ \text{Total Cost} = 20 \times 4.86 = 97.2 \, \text{USD} \]

Final Answer