find length of square side??

Question

How do you find the length of the side of the square, when the square is inscribed in a right triangle. solve in terms of a, x and b . a and b are sides of the right triangle. x is the length of the side.

(it'd be better if i could draw a picture but i cant. :/)

Answer 1

Square is inscribed within right angled triangle of sides a and b.
Area of triangle = (1/2) a b

Inside the triangle then have:-
square of area x²
triangle of area (1/2) (x) (b - x)
triangle of area (1/2) (x) (a - x)

(1/2) (x) (b - x + a - x) = (1/2) ab
x (b + a) = ab
x = (ab) / (a + b)

Answer 2

okay. I think I know what you are saying. The length that they are asking you to find is one of the 4 sides of the square. That same side is also shown as the longest side of the triangle.

To solve this you need to use the equation a^2+b^2=c^2.
(c=x)

For example, the lengths that you know are 6 and 2. You take 6 squared, which is 36. Then add 2 squared, which is 4. That totals up to 40. Then find the square root of 40, that would be the answer.

So just do what I just did, but use your numbers instead.

Answer 3

Here is a site with an example
http://www.math.nmsu.edu/~breakingaway/Lessons/sit/sit.htm

basically, you take the area of the triangle (ab/2) and subtract off the area of the 2 smaller triangles {(a-x)x/2} and {(b-x)x/2}. This gives you the area of the square. take the square root of that expression, and that is equal to x

Answer 4

a*a + b*b=c*c where c is the hypotenuse of a right triangle. If you have 2 sides of a right triangle you can always solve for the missing side using this formula.

Answer 5

Path Agrius Theorem baby ... a squared plus b squared equal c squared. Piece of cake.

Answer 6

If a=b=1;
then: a=a
then: x=1/2

Answer 7

http://s5.photobucket.com/albums/y164/azianshrimp/?action=view¤t=SquareInscribedInsideaRightTriangle.jpg