Question 1206101
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The sum of the length and width of the given rectangle is 175 yards.<br>
For another rectangle to have the same perimeter, the sum of its length and width has to be 175 yards also.<br>
The area of a rectangle is the product of the length and width.<br>
For a fixed sum of two numbers, the product of the two numbers is larger if the two numbers are close together and smaller if the two numbers are farther apart.  The product is maximum if the two numbers are the same.<br>
So the rectangle with the largest area and with the same perimeter as the given rectangle is a square with side length 175/2 = 87.5.<br>
Some other dimensions of a rectangle with the same perimeter as and larger area than the given rectangle are...
70 x 105
75 x 100
87 x 88
...<br>
Or, in general, any two numbers of the form (87.5+x) and (87.5-x), where x is any non-negative number less than 87.5.<br>