Answer:
The length of the box is 9 meters
Step-by-step explanation:
The formula of a Right Rectangular Prism is
V=L*W*H
Where,
L= the length
W=the width
H= the height
In this case,
V =270 m³
height=5 m
width = length-3m
Isolating the Length
V=L*W*H
L=V/W*H
L=V/(L-3)*H
L*(L-3)=V/H
L²-3L= 270/5
L²-3L= 54
L²-3L-54= 0
We can use Quadratic Formula.
If we have an equation with the following Standard Form , ax² + bx + c = 0
we can solve the equation applying the Quadratic Formula.
x = (−b ± √(b^2 − 4ac))/ 2a
In this case
a=1
b=-3
c=-54
x = (3 ± √(-3^2 − 4*1*-54))/ 2*1
x = (3 ± √(9 + 216))/ 2
x = (3 ± √(225))/ 2
x = (3 ± 15)/ 2
x = (3 - 15)/ 2 x = -12/2=-6 can´t be negative
x = (3 + 15)/ 2 x = 18/2=9
