Answer:
x = 4sqrt6
Step-by-step explanation:
lets name the perpendicular line on the inside of the triangle, z ;and the side length adjacent to the side with length x, y.
We can identify Pythagorean equations from this as there are 3 different right triangles:
x^2 + y^2 = 12^2
z^2 + 8^2 = x^2
4^2+z^2 = y^2
hey! we can substitute the x^2 and y^2 into the first written equation!
so we have:
(z^2+8^2) + (4^2+z^2) = 12^2
2z^2+64+16 = 144
2z^2+80 = 144
2z^2 = 64
z^2 = 32
since there's an equation that allows us to use z^2 to find x (well x^2) we can stop here and don't have to square root to find z,
(32) + 6^2 = x^2
32 + 64 = x^2
96 = x^2
sqrt96 = x (now we have to square root)
4sqrt6 = x (see the attached pic for the square root tree method)
