What is the value of x

Triangle with sides 10 6 x-6

Given that the triangle is a right angled triangle, to solve for x we shall use the Pythagorean theorem given by:

c^2=a^2+b^2

where:

c is the hypotenuse

a and b are the legs.

c=10

a=6

b = (x-6)

thus plugging the values in the equation and solving for x we get:

10^2=6^2 + (x-6) ^2

100=36+x^2-12x+36

100=x^2-12x+72

0=x^2-12x-28

factoring the above we get:

0 = (x+2) (x-14)

hence

x=-2 or x=14

given that there is no negative distance then

x=14

thus the value of x is 14