The total surface area of a box is 100. The length of the box is twice its width, as well as 3 less than its height. How many units are in the height of the box?
+23246 Call the width: W
Call the length: L The length is twice the width: L = 2W
Call the height: H The length is 3 less than the height: L = H - 3 ---> H = L + 3 ---> H = 2W + 3
The total surface area = 100.
The total surface ares = 2LW + 2LH + 2Wh = 100
---> LW + LH + WH = 50
Substituting:
---> 2W·W + 2W·(2W + 3) + W·(2W + 3) = 50
---> 2W2 + 4W2 + 6W + 2W2 + 3W = 50
---> 8W2 + 9W - 50 = 0
---> (8W + 25)(W - 2) = 0
---> W = 2 or W = -25/8 (impossible)
---> W = 2 and L = 4 and H = 7
