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Correct Answer: 56.25%
to determine what percentage of the yard will not be fenced in, we first need to calculate the area that the owner wants to fence. the dimensions given are 20 yards by 35 yards. multiplying these dimensions gives us the area of the space that will be fenced:
\[ 20 \, \text{yd} \times 35 \, \text{yd} = 700 \, \text{sq yd}. \]
next, we know the total area of the yard is 1600 square yards. to find out how much of this area will not be fenced, we subtract the fenced area from the total area:
\[ 1600 \, \text{sq yd} - 700 \, \text{sq yd} = 900 \, \text{sq yd}. \]
now, to find the percentage of the yard that will not be fenced in, we divide the unfenced area by the total area and then multiply by 100 to convert the decimal into a percentage:
\[ \left(\frac{900 \, \text{sq yd}}{1600 \, \text{sq yd}}\right) \times 100\% = 56.25\%. \]
therefore, 56.25% of the yard will not be fenced in. this calculation shows that a significant portion of the yard remains open, providing more space for other activities or future landscaping projects.
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