Imagine you are an apprentice in a sail-making shop. A customer needs a replacement right-triangular sail with a hypotenuse of 17 feet, where the shorter leg is 7 feet less than the longer leg. To calculate the dimensions, you use the variable $x$ for the longer leg. Match each part of the sail's design to its correct mathematical or numerical value based on the standard problem-solving setup.

A technician is drafting the dimensions for a replacement right-triangular sail. The diagonal edge (hypotenuse) of the sail is 17 feet long. One of the legs is 7 feet less than the other leg. If $x$ represents the length of the longer leg, which equation correctly translates this relationship using the Pythagorean Theorem?

A technician at a sailmaking company is using a standard seven-step strategy to verify the dimensions of a right-triangular sail with a 17-foot hypotenuse. Arrange the following tactical steps in the correct order as prescribed by the strategy.

Evaluating a Sail Dimension Report

During the drafting process for a right-triangular sail, a technician factors the necessary quadratic equation to find the sail's missing dimensions and calculates the possible mathematical solutions to be $x = 15$ and $x = -8$. The technician must discard the solution $x = -8$ because a physical ________ cannot be a negative value.

Evaluating Mathematical Solutions for Sail Dimensions

A lofting designer at a commercial sail workshop is drafting a right-triangular sail. The diagonal edge (hypotenuse) must measure exactly 17 feet, and one leg must be 7 feet shorter than the other leg (represented by $x$). During the translation step of the design audit, the designer correctly models this relationship using the equation $x^2 + (x - 7)^2 = 17$.