A farmer wants to create a rectangular fence for his goats that is 12 yd. by 15 yd. Inside the same area, the farmer will also build a small rectangular fenced garden that is 3 yd. by 6 yd. If the goats are not allowed in the garden, how many square yards is the fenced area that the goats will be allowed to roam in?(1 point)

Question

Responses

162 yd2
162 yd2

180 yd2
180 yd2

18 yd2
18 yd2

198 yd2

Answer 1

To find the area where the goats are allowed to roam, we first calculate the total area of the rectangular fence for the goats and then subtract the area of the garden.

1. Calculate the area of the goat pen: \[ \text{Area of goat pen} = \text{length} \times \text{width} = 12 , \text{yd} \times 15 , \text{yd} = 180 , \text{yd}^2 \]

2. Calculate the area of the garden: \[ \text{Area of garden} = \text{length} \times \text{width} = 3 , \text{yd} \times 6 , \text{yd} = 18 , \text{yd}^2 \]

3. Subtract the area of the garden from the area of the goat pen to find the area where the goats can roam: \[ \text{Area for goats} = \text{Area of goat pen} - \text{Area of garden} = 180 , \text{yd}^2 - 18 , \text{yd}^2 = 162 , \text{yd}^2 \]

Therefore, the fenced area that the goats will be allowed to roam in is 162 yd².