Help with stupid simple math problem.

[commasense]

I think I used to know this, and I know I should be able to figure it out, but my high school math skills have atrophied over the past 40 years.

What's the method for finding factors of a given number that are in a certain ratio to each other? For instance, a movie theater screen is said to be 180 square meters in area. Assuming that its sides are in a 1.78 ratio (the width is 1.78 times the height), how do I determine their dimensions?

Thanks.

[Cabbage]

Let h and w be width and height, respectively.

You're given:

hw = 180

w=1.78h

Substitute:

h(1.78h) = 1.78h^2=180

Solve for h: sqrt(180/1.78)

[The Hamster King]

Area = Width x Height
Width = Height x 1.78



So, substituting the second equation into the first:

Area = Height x Height x 1.78



And solving for Height:

Height = Square Root( Area / 1.78 )

[Giles]

If x is the shorter dimension, then

1.78 x^2 = 180

x^2 = 101.1236

x = 10.05602 metres

and the other side is 17.89972 metres.

[commasense]

(I had that response all ready to go.)

Thanks, guys.

(Now can someone help me figure out how much 2+2 is?)

[Malacandra]

How much would you like it to be?

[Chronos]

2 + 2 = 1 modulo 3.

[DSYoungEsq]

5 (for very large values of 2)