Re: Right Triangle: Unable to find a solution for...



On Sun, 1 Oct 2006, Auto wrote:

Knowing only the area of a right triangle, is it possible to calculate the
length of the hypotenuse or the sides?

Example: Area=38.5
Hypotenuse ? Sides ?

Or, Knowing only the hypotenuse of a right triangle, is it possible to
calculate its area?

Example: Hypotenuse = sqrt(34);

It looks strange to me, but actually it seems that a parameter is missing,
so that the triangle is not characterize.

Your suspicion is correct: not enough data (and others have elaborated on
that).

Something is possible: given both area A and hypotenuse c, you can decide
by calculation if there is such a right triangle, and if there is one,
what its legs (sides) (a and b such that a^2+b^2=c^2) are.

Your pair of data (A=38.5 and c=sqrt(34)) gives an example where such a
triangle does not exist. Why?

a^2 + b^2 = c^2
a*b/2 = A

Combine these two to obtain

(a-b)^2 = c^2 - 4*A

In your example, c^2 - 4*A = 34 - 154 = -120

and the square of a real number cannot be negative.

If you also find (a+b)^2 (do it yourself), you can recover a and b.

Cheers, ZVK(Slavek).
.

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