# Calculate width and Height of rectangle containing given area and conforming to given ratio

My algebra is sooo rusty so this should be an easy one!

Area of a rectangle is

A = W x H

If you're given A (say 150) and a ratio of W:H (say 3:2) how can you calculate W and H?

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Right so you have $W:H$ is $3:2$, which means $$150 = 3x \times 2x$$ So this is just a simple equation which you can solve for. That is $6x^{2}=150$ which says $x^{2} =25$ and hence $x =\sqrt{25}$ that is $x =5$. So $W = 3 \times 5 =15$ and $H= 2 \times 5 =10$ and you can see that they have ratio $3 : 2$.

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X=5 (then you get 3x * 5x = 15x10 = 150) - but you're showing X = 5 srt 2 - is that correct? –  Ryan Nov 18 '10 at 23:42
@Ryan: Edited now. Sorry made a egregious mistake –  anonymous Nov 18 '10 at 23:50
Cheers - skool is coming back to me after many years ;) Got stuck with simplifying 3x X 2x => 3 X x X 2 X x => 6x X x => 6x^2. Also found this algebrahelp.com/calculators/equation/calc.do?equation=150%3D3x*2x&sol‌​vf=AUTO –  Ryan Nov 19 '10 at 0:02
HINT $\rm\displaystyle\ \ \frac{W}H = \frac{3}2\ \Rightarrow\ 2\:W = 3\:H\:,\$ so $\rm\ 300 = 2\:W\:H = 3\:H\:H\ \Rightarrow\ H = \ldots$