Question 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 smaller garden, how many square yards is the fenced area that the goats will be allowed to roam in? (1 point) Responses 162 yd2 162 yd2 52 yd2 52 yd2 62 yd2 62 yd2 152 yd2

1 answer

To find the area that the goats are allowed to roam in, we first need to calculate the area of the larger fenced area and then subtract the area of the smaller garden.

  1. Calculate the area of the larger fenced area for the goats: \[ \text{Area}_{\text{goats}} = \text{length} \times \text{width} = 12 , \text{yd} \times 15 , \text{yd} = 180 , \text{yd}^2 \]

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

  3. Calculate the area available for the goats: \[ \text{Area}{\text{goats allowed}} = \text{Area}{\text{goats}} - \text{Area}_{\text{garden}} = 180 , \text{yd}^2 - 18 , \text{yd}^2 = 162 , \text{yd}^2 \]

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