Find the value of x

14 viewed last edited 4 years ago
Hanna Owens
There is a right triangle, its hypoteneuse is 4x-6 the base is 3x and the shortest side is x+6. Find the value of x. How do I do this? I am having a total brainfart and can't figure it out.
Vivekanand Vellanki
Pythagorus theorem states that in a right triangle, a^2+b^2=c^2 where c is the hypotenuse and a and b are the other two sides. Applying this, you get (3x)^2+(x+6)^2=(4x-6)^2 9x^2 + x^2 + 12x + 36 = 16x^2 - 48x +36 10x^2 + 12x + 36 = 16x^2 - 48x + 36 0 = 6x^2 - 60x 6x(x-10)=0 Hence, x is either 0 or 10. x=0 leads to one of the sides being 0. Hence, x is 10.