First label all the sides with letters:longest side = amiddle length side = bshortest side = cNow convert the question into equation form: "the longest side is two units more than the shortest side" becomes, a = 2 + c (1)"middle length side is one unit longer than the shortest side" becomes, b = 1 + c (2)"The total surface area of the cuboid is 52 units² " becomes, 2ab + 2ac + 2bc = 52 (3)Substitute expressions (1) and (2) into (3) to get2(2+c)(1+c) + 2c(2+c) + 2c(1+c) = 52Expand out the brackets:2(2+3c+c^2) + 4c + 2c^2 + 2c + 2c^2 = 52which becomes:4 + 6c + 2c^2 + 6c + 4c^2 = 52collect all the terms together:6c^2 + 12c - 48 = 0Divide by 6 to simplify equation:c^2 + 2c - 8 = 0factorise this equation into brackets to find c, by finding two numbers that multiply together to make -8, and add together to make 2... i.e. 4 and -2,(c + 4)(c-2) = 0Therefore, c = -4, or c=2. Since c must be positive (a negative side length would make no physical sense) c must be 2. We can then subsitute this back into (1) and (2) to find values for a and b, a = 4b = 3and then double check that the surface area is 52.