37. A rectangular yard has a length that is 7 feet longer than its width. If the perimeter of the yara is 46 feet, what is the area of the yard?

Step 1 ：Translate the problem into mathematical equations. We know that the length (l) is 7 feet longer than the width (w), so we can write this as \(l = w + 7\). We also know that the perimeter (P) is 46 feet, and the formula for the perimeter of a rectangle is \(2l + 2w = P\). Substituting \(l = w + 7\) into the perimeter equation gives us \(2(w + 7) + 2w = 46\).

Step 2 ：Solve the equation \(2(w + 7) + 2w = 46\) for w. This simplifies to \(4w + 14 = 46\), and further simplifies to \(4w = 32\). Dividing both sides by 4 gives us \(w = 8\).

Step 3 ：Substitute \(w = 8\) into the equation \(l = w + 7\) to find the length. This gives us \(l = 8 + 7 = 15\).

Step 4 ：Finally, substitute \(l = 15\) and \(w = 8\) into the area formula \(A = lw\) to find the area. This gives us \(A = 15 \times 8 = 120\).

Step 5 ：Final Answer: The area of the yard is \(\boxed{120}\) square feet.