we have that
The volume of a rectangular prism is given by the formula
[tex]V=L*W*H[/tex]
where
V=252 cm3
H=3 cm
W=x cm
L=W+5 --------> L=x+5
substitute given values in the formula
[tex]\begin{gathered} 252=(x+5)(x)(3) \\ 252=3x^2+15x \\ 3x^2+15x=252\text{ ---> equation that models the volume} \end{gathered}[/tex]
Solve the quadratic equation
using the formula
[tex]3x^2+15x-252=0[/tex]
a=3
b=15
c=-252
substitute
[tex]x=\frac{-15\pm\sqrt{15^2-4(3)(-252)}}{2(3)}[/tex][tex]x=\frac{-15\pm57}{6}[/tex]
The values of x are
x=7 cm and x=-12 cm ( is not a solution because is a negative number)
The width is 7 cm
therefore
Is not possible for the width to be 7.5 cm
