A train gutter is made from sheets of aluminum that are 26 inches wideThe edges are turned up to form right anglesDetermine the depth of the gutter that will allow a cross-sectional area of 54 square inchesThere are two solutions for this problemRound to the nearest tenth of an inch.
Start with the two variables: x represents the height of each side of the gutter y represents the width of the bottom of the gutter therefore, we get 2 equations: xy54 (the number of square inches we are asked to find) and 2x+y26 (the length of the 2 sides plus the length of the bottom) simplify the bottom equation and we get: y26-2x substitute y in the first equation and we get: x(26-2x)54 : 26x-2x?54 put into the form ax?+bx+c0, we get: x?-13x+260 feeding this into the quadratic equation (see link below), we get two answers for x: x 10.5 and 2.5 (rounded to the nearest tenth) put that into the first equation (2x+y26), and y becomes y 5 and 21 respectively
