Answer:
Height of the box = 11.5 in
Step-by-step explanation:
Let h be the height of the box.
Assuming the volume of the Box is [tex]258.75\ in^3[/tex].
Given:
Length = Height - 4 = h - 4
Width = 3 in
We need to find the height of the box.
Solution:
We know that the volume of the box.
[tex]Volume = Length\times height\times width[/tex]
Substitute all given value in above formula.
[tex]258.75 = (h-4)\times h\times 3[/tex]
Rewrite the equation as:
[tex]258.75 = 3h(h-4)[/tex]
[tex]258.75 = 3h^2-12h[/tex]
[tex]3h^2-12h-258.75=0[/tex]
whole equation divided by 3.
[tex]h^2-4h-86.25=0[/tex]
Use quadratic formula with [tex]a = 1, b = -4,c=-86.25[/tex]
[tex]h=\frac{-b\pm \sqrt{(b)^{2}-4ac}}{2a}[/tex]
Put these a, b and c value in above equation.
[tex]h=\frac{-(-4)\pm \sqrt{(-4)^{2}-4(1)(-86.25)}}{2(1)}[/tex]
[tex]h=\frac{4\pm \sqrt{16+345}}{2}[/tex]
[tex]h=\frac{4\pm \sqrt{361}}{2}[/tex]
[tex]h=\frac{4\pm 19}{2}[/tex]
For positive sign
[tex]h=\frac{23}{2}[/tex]
h = 11.5 in
For negative sign
[tex]h=\frac{-15}{2}[/tex]
h = -7.5
We take positive value of h.
Therefore, the height of the box h = 11.5 in
