Answer:
[tex]y = 2\sqrt{10}[/tex]
Step-by-step explanation:
In left small right triangle: we have the square of left side = 5^2 + y^2 = 25 + y^2
In right small right triangle: we have the square of right side = 8^2 + y^2 = 64 + y^2
In the large right triangle, we have (25 + y^2) + (64 + y^2) = (5 + 8)^2
89 + 2y^2 = 13^2 = 169
2y^2 = 169 - 89 = 80
y = 80/2 = 40
so
[tex]y=\sqrt{40} = 2\sqrt{10}[/tex]
