Ametal worker traced a triangular piece of sheet metal on a coordinate plane as shown

The coordinates of vertices of the triangle can be seen from the graph. Using these vertices we can find out the length of sides and hence we can find the longest side of the triangle.

The triangle is a Right Angled Triangle. In a right angled triangle the length of hypotenuse is always larger than the base and perpendicular. The end points of the hypotenuse are (2,4) and (-3,-2). Using the distance formula, we can find the length of hypotenuse:



Thus the length of longest side of the metal triangle is 7.8 inches, rounded to nearest tenth of an inch.