\( \triangle J K L \sim \triangle S T U \). The ratio of \( S T \) to \( J K \) is \( 5: 2 \). The perimeter of \( \triangle S T U \) is 35 feet. Find the perimeter of \( \triangle J K L \).

Since the triangles \( \triangle J K L \) and \( \triangle S T U \) are similar, the ratio of their corresponding sides is the same as the ratio of their perimeters. Given that the ratio of \( S T \) to \( J K \) is \( 5:2 \), we can express this ratio as: \[ \frac{S T}{J K} = \frac{5}{2} \] Let the perimeter of \( \triangle J K L \) be denoted as \( P_{JKL} \) and the perimeter of \( \triangle S T U \) be denoted as \( P_{STU} \). Since the triangles are similar, we have: \[ \frac{P_{STU}}{P_{JKL}} = \frac{5}{2} \] We know that the perimeter of \( \triangle S T U \) is 35 feet, so we can substitute this value into the equation: \[ \frac{35}{P_{JKL}} = \frac{5}{2} \] To solve for \( P_{JKL} \), we can cross-multiply: \[ 35 \cdot 2 = 5 \cdot P_{JKL} \] This simplifies to: \[ 70 = 5 \cdot P_{JKL} \] Now, divide both sides by 5: \[ P_{JKL} = \frac{70}{5} = 14 \] Thus, the perimeter of \( \triangle J K L \) is \[ \boxed{14} \text{ feet.} \]