Julia needs to make a box in the shape of a rectangular prism with a height of 3 inches and a volume of 243 cubic inches. The di
mensions, in inches, must be whole numbers greater than 1. Julia claims that the length and the width must be equal. Part A: What dimensions would support Julia's claim about the length and with of the box? Part B: What dimensions would not support Julia's claim about the length and width of the box. Part A length =______________ Part A width=_____________________. Part B length_________________Part B Width=_____________________.
The volume of a rectangular prism is equal to length*width*height. In this case, we have V = 243 and H = 3. 243 = LW(3), so LW = 81, where L & W are whole numbers greater than 1. There are only 3 possible pairs of values for this: 27*3, 9*9, and 3*27 (we cannot use 1*81 or 81*1, since we need dimensions > 1). Part A. This could be true if Length = 9 in and Width = 9 in, as 9*9 = 81. Part B. The claim could be false if Length = 27 in and Width = 3 in, as 27*3 = 81, but 27 is not equal to 3. *Note that the width cannot be longer than the length.
The number D = b2 – 4ac determined from the coefficients of the equation ax2 + bx + c = 0. The discriminant reveals what type of roots the equation has. Note: b2 – 4ac comes from the quadratic formula.
