Respuesta :
Answer:
Length of box is(l) =2 ft
width of box is (w) = 3 x - 5 =3(3)-5 = 9-5=4
height of box is (h) = 2 x - 1 =2(3)-1 = 6 -1 =5
Step-by-step explanation:
Step 1:-
Volume of the box is V= l w h
Given Volume of the box is V = 40 ft^3
given 2 × (3 x-5)×(2 x-1) =40..........(1)
Step 2:-
simplification [tex](6 x-10)(2 x-1)=40[/tex]
[tex]12 x^{2} -6 x-20 x+10 =40[/tex]
[tex]12 x^{2} -20 x -6 x -30=0[/tex]
take common 2
[tex]2(6 x^{2} -13 x -15)=0[/tex]
Find factors
[tex]6 x^{2} -18 x+5 x-15=0[/tex]
[tex]6x(x-3)+5(x-3)=0[/tex]
[tex](6 x+5)(x-3)=0[/tex]
x=[tex]\frac{-5}{6} and x=3[/tex]
Step 3:- The value of x [tex]\frac{-5}{6}[/tex] is not satisfied
the value of x =3 is satisfied in equation(1)
Therefore the length of the box is l = 2
the width of the box is w = 3 x-5=3(3)-5=9-5=4
The height of the box is h= 2 x-1 = 2 (3) -1 =5
Verification:-
V = 2(4)(5) =40
In the given problem volume is 40 so both are equal
Answer:- The length of the box is l = 2
The width of the box is w =4
The height of the box is h= 5
