Thread: figuring out height/width from area

hello everyone
i have a rectangle that is 14*18
which is 252 sq. in.

i need to get the H&W of a rectangle that its area is some percent of 252 (lets say half)
so what will the H&W be for 126 sq.in. if it would have the same ratio as 14*18?

thank you very much

i need the formula, not the answer for this specific example

Originally Posted by yisman

hello everyone
i have a rectangle that is 14*18
which is 252 sq. in.

i need to get the H&W of a rectangle that its area is some percent of 252 (lets say half)
so what will the H&W be for 126 sq.in. if it would have the same ratio as 14*18?

thank you very much

i need the formula, not the answer for this specific example

1. Let H, W denote the original height and width of the rectangle and h, w the height and width of the transformed rectangle. Then you know





2. The area of the original rectangle is:

and the area of the transformed rectangle is:


3. With your example:


Plug in into the equation above:

thanks
it was that sqr root that i needed!
where do i "mark as answer"?
thanks again

So really, you need a formula for side lengths of a given ratio; also given is area.
a = area (126 in your example), ratio = u/v (14/16 = 7/9 in your example).
x,y = side lengths

General case formula: x = SQRT(au / v) ; y = a / x

With your example:
x = SQRT(126*7/9) = 7SQRT(2)
y = 126 / 7SQRT(2) = 9SQRT(2)

thanks
ur formula is better, as i needed it for a program script, which doesnt realy accept latex... :-)
thnak you

Originally Posted by yisman

ur formula is better, ......

For your benefit: use "your", NOT "ur".