a)
The box is a rectangular prism. The base measures 2x + 5 by x.
The area of the base is length times width, or (2x + 5) * x = 2x^2 + 5x.
The area of the base is 58, so
2x^2 + 5x = 58
Subtract 58 from both sides.
2x^2 + 5x - 58 = 0
b)
[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]
[tex] x = \dfrac{-5 \pm \sqrt{5^2 - 4(2)(-58)}}{2(2)} [/tex]
[tex] x = \dfrac{-5 \pm \sqrt{25 + 464}}{4} [/tex]
[tex] x = \dfrac{-5 \pm \sqrt{489}}{4} [/tex]
[tex] x = \dfrac{-5 + \sqrt{489}}{4} [/tex] The other answer is negative and can be discarded.
[tex] x = \dfrac{-5 + 22.11}{4} [/tex]
[tex] x = 4.28 [/tex]
x = 4.28
c) The volume of the box is the area of the base multiplied by the height.
The height is x - 2. 4.28 - 2 = 2.28. The height is 2.28 cm.
V = 58 * 2.28
V = 132.14
The volume is 132.14 cm^3
