Box construction An open box is made from a 10cm by 20cm pie

Box construction An open box is made from a 10-cm by 20-cm piece of tin by cutting a square from each corner and folding up the edges. The area of the resulting base is 96 cm^2. What is the length of the sides of the squares?

Solution

Let the side of the square be x cm. The area of the 10 cm by 20 cm piece of tin , before cutting the square corners is 10*20 = 200.cm². After cutting the square corners and after folding the sides, the area of the base is 96 cm². The measure of the base remaining after folding the corners is 10 - 2x cm by 20 - 2x cm. Thus, (10- 2x) (20 -2x) = 96 or, 200 - 20x - 40 x + 4x² = 96 or, 4x² - 60x + 200 = 96 or, 4x² - 60x + 200 - 96 = 0 or, 4x² - 60x + 104 = 0 or, on dividing both the sides by 4, we have  x² - 15x + 26 = 0 or, x² - 13x -2x + 26 = 0 or, x(x -13) -2(x -13) = 0 or, (x -13)(x -2) = 0. Thus, either x = 13 or x = 2. Now, x cannot be 13 as one side of the tin piece , before cutting the corners, is 10 cm. Hence x = 2, i.e. the length of the side of the squares is 2 cm. We can verify the result by multiplying 10 -2* 2 by 20 – 2*2, i.e. 6 by 16 which is 96 cm² Thus, our result is correct.