85. Building Lots. A lot for sale in New York City is in the shape of a right triangle, as shown below. The side not bordering a street is 25 ft long. One of the other sides is 5 ft longer than the remaining side. Find the lengths of the sides.

To tackle this triangle problem, let’s assign some variables. Let the shorter side adjacent to the 25 ft side be \( x \). Consequently, the longer side (the one that's 5 ft longer) would be \( x + 5 \). By applying the Pythagorean theorem, where the sides of the right triangle satisfy \( a^2 + b^2 = c^2 \), with 25 ft as the hypotenuse, you can set up the equation: \( x^2 + (x + 5)^2 = 25^2 \). From here, you can solve for \( x \) to find the lengths of all sides of the triangle! Something to keep in mind is the importance of double-checking your equations and ensuring that your calculations are spot on. Mistakes often creep in during algebraic manipulations, especially when squaring terms or applying the Pythagorean theorem. Always simplify step-by-step, and don't hesitate to use a calculator for the final checks!