SOLUTION: if a rectangles diagonal is 32 inch what will be its length

Question 906830: if a rectangles diagonal is 32 inch what will be its length

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you don't have enough information to determine this exactly.

the diagonal of a rectangle is equal to 32.

by the pythagorean formula, the diagonal squared of the rectangle is equal to its length squared plus its width squared.

solve for it's length and you get it's length is equal to the square root of (it's length squared minus its width squared).

in algebraic terms, this looks like L^2 = (32^2 - W^2)

you can pretty much pick any W^2 that is less than 32^2 and you will get a corresponding length that will satisfy the equation.

assuming W^2 = 31^2, you will find a corresponding L^2 that is equal to 63.

if L^2 is equal to 63, then L is equal to sqrt(63)

you have a length of sqrt(63) and a width of 31 and a diagonal of 32.

31^2 + sqrt(63)^2 = 32^2 becomes 961 + 63 = 1024 which becomes 1024 = 1024 which confirms that the solution of L^2 = 63 is correct.

pick any other value of W^2 less than 32^2 and you'll get another value of L that will satisfy the equation.

now if you're talking about a square rather than a rectangle, then you can solve for the length of a side because length and width are now the same measure.

in that case you get s^2 + s^2 = 32^2 which becomes 2s^2 = 32^2 which gets you s^2 = 512 which gets you s = sqrt(512), s being the length of a side of the square.

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