Answer:
[tex]x=\sqrt{40}, y=\sqrt{104}[/tex]
Step-by-step explanation:
Note the triangle formed by x, y, and 8 is similar to the largest triangle
so x : c = 8 : y = y : 13, where c is the rightmost vertical length, c² = x² + 5²
From 8 : y = y : 13, we get
y² = 13*8 = 104, so
[tex]y=\sqrt{104}[/tex]
From x : c = 8 : y, we have xy = 8c
x²y² = 64c²
104x² = 64(25 + x²)
104x² = 1600 + 64x²
40x² = 1600
x² = 40
[tex]x=\sqrt{40}[/tex]