A carpenter is creating two new templates for his designs.

Last updated: 7/18/2022

A carpenter is creating two new templates for his designs. One template will be in the shape of a right triangle, where the longer leg is three inches more than three times the shorter leg. The second template will be in the shape of a rectangle, where one side length is one inch less than three times the length of the triangle's shorter leg, and the other side length is one inch more than twice the width. The carpenter needs the lengths of both diagonals to be the same. Write a system of equations to represent this situation, where y is the length of the diagonals, and x is the shorter leg of the triangle. Which statement describes the number and viability of the system's solutions? A. The system has two solutions, and both are viable because they result in figures with only positive side lengths. B. The system has two solutions, but only one is viable because the other results in a figure with negative side lengths. C. The system has only one solution, and it is viable because it results in a figure with only positive side lengths. D. The system has only one solution, but it is not viable because it it results in a figure with a negative side length.