<PRE><B>Question 1114397</B>
The diagonal of a rectangle forms a right triangle with the sides of the rectangle.  So we can use the Pythagorean Theorem to solve the problem.&lt;br&gt;
If we blindly plug in numbers, the algebra would look like this:&lt;br&gt;
{{{x^2 + (2x-2)^2 = 34^2}}}
{{{x^2 + 4x^2-8x+4 = 1156}}}
{{{5x^2-8x-1152 = 0}}}&lt;br&gt;
Then use any of a number of methods of solving that equation to find the positive root.&lt;br&gt;
The problem is far more easily solved if you use Pythagorean triples -- sets of 3 integers that can be the side lengths of a right triangle.&lt;br&gt;
The problem says the diagonal of the rectangle is 34 yards.  Not approximately 34 yards -- exactly 34 yards.  Therefore we want a Pythagorean triple with the largest number 34.&lt;br&gt;
34 is 2 times 17, and a common Pythagorean triple is (8,15,17).  So the side lengths of the right triangle formed by the lawn and its diagonal are 16, 30, and 34.&lt;br&gt;
And indeed 16 is the positive solution to that ugly quadratic equation shown above.&lt;br&gt;
Answer:  The lawn is 16 yards by 30 yards.</PRE>