Final answer:
To find the dimensions of the open rectangular box, we can use the given base area of 58cm^2. By setting up and solving an equation, we can find the value of x, which will help us determine the length, width, and height of the box.
Step-by-step explanation:
The base of the open rectangular box has a length of (2x+5)cm and a width of xcm. The area of the base is given as 58cm^2. The height of the box is (x-2)cm.
To find the dimensions of the box, we can use the given information of the base area. The length multiplied by the width should give us the area. So, we have the equation (2x + 5)(x) = 58cm^2.
To solve this equation, we need to expand it and set it equal to zero. By rearranging the terms, we get 2x^2 + 5x - 58 = 0. We can then factor this quadratic equation to find the values of x. Once we have the value of x, we can substitute it back into the expressions for the length, width, and height of the box to get the final dimensions.