SOLUTION: If x,y,z are sides of right angled triangle where z is the hypotenuse then express the product of the sumof x and z and the difference of z and x in one variable form

Algebra ->  Linear-equations -> SOLUTION: If x,y,z are sides of right angled triangle where z is the hypotenuse then express the product of the sumof x and z and the difference of z and x in one variable form      Log On


   

Question 1199484: If x,y,z are sides of right angled triangle where z is the hypotenuse then express the product of the sumof x and z and the difference of z and x in one variable form
Answer by math_tutor2020(3817) About Me  (Show Source):
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the sum of x and z translates to x+z
the difference of z and x means we have z-x

The product of those two lines is the multiplication of each
(x+z)*(z-x)
(z+x)*(z-x)
z^2-x^2

We have a difference of squares.
The pythagorean theorem deals with squared numbers.
a^2+b^c = c^2
x^2+y^2 = z^2
y^2 = z^2-x^2

Answer: y^2