Golden Rectangle Wordproblem - Help

[mcruz65]

Golden Rectangle. The so-called golden rectangle is said to be extremely pleasing visually and was used often by ancient Greek and Roman architects. The length of a golden rectangle is approximately 1.6 times the width. Find the dimensions of a golden rectangle if its area is 9000 m^2.

w = the width of the rectangle and 1.6w = the length

Area = length x width

w x 1.6w = 9000 m^2

1.6w^2 = 9000 m^2

sqrt(1.6w^2) = sqrt(9000 m^2)

1.6w = 9000m

1.6w/1.6 = 9000m/1.6

w = 5625

Is this correct??

 

[JuicyBurger]

w = the width of the rectangle and 1.6w = the length

Area = length x width

w x 1.6w = 9000 m^2< yes

1.6w^2 = 9000 m^2< yes

sqrt(1.6w^2) = sqrt(9000 m^2)<yes

1.6w = 9000m<No --Right here you take the square root of the \(\displaystyle w^2\) and the \(\displaystyle m^2\)

1.6w/1.6 = 9000m/1.6

w = 5625
Is this correct??[/quote]


What you did was take the square root of the width and the UNITS of 9000. m^2 is just meters squared, they are just units... This is how it should have turned out:

\(\displaystyle 1.6w^2 = 9000 m^2\)

\(\displaystyle w^2 = 9000/1.6\)

\(\displaystyle w = \sqrt{\frac{9000}{1.6}}\)

Do you see where you went wrong?

I hope this helps some