SOLUTION: Volume= 126ft^3 Height = x Length = x+3 Width = x+4 What is x?

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Volume= 126ft^3 Height = x Length = x+3 Width = x+4 What is x?       Log On


   

Question 943435: Volume= 126ft^3
Height = x
Length = x+3
Width = x+4
What is x?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

V=L%2AW%2Ah
if
Volume=+126ft%5E3
Height h=+x
Length L=+x%2B3
Width W=+x%2B4
then
126=%28x%2B3%29%2A%28x%2B4%29%2Ax
126=%28x%5E2%2B4x%2B3x%2B12%29%2Ax
126=x%5E3%2B7x%5E2%2B12x
0=x%5E3%2B7x%5E2%2B12x-126........write 7x%5E2 as -3x%5E2%2B10x%5E2 and 12x as -30x%2B42x
x%5E3-3x%5E2%2B10x%5E2-30x%2B42x-126=0...group
%28x%5E3-3x%5E2%29%2B%2810x%5E2-30x%29%2B%2842x-126%29=0
x%5E2%28x-3%29%2B10x%28x-3%29%2B42%28x-3%29=0
%28x-3%29%28x%5E2%2B10x%2B42%29=0
real root is:
if %28x-3%29=0 => x=3
here %28x%5E2%2B10x%2B42%29=0 we have a=1, b=10 and c=42
since c%3Eb, determinant b%5E2-4ac is negative, so we will have two complex roots and we do not need them for length and width
so, we will use x=3
then
Height h=+3ft
Length L=+6ft
Width W=+7ft
check the volume:
V=L%2AW%2Ah
V=6ft%2A7ft%2A3ft
V=126ft%5E3 which is same as given