Answer:
[tex]y=20\sqrt{1}[/tex]
Step-by-step explanation:
The construction of the figure gives us three right triangles, where we can apply Pythagora's Theorem.
I have added two variables to the image in the picture attached.
On the triangle with sides y,h,16 we have:
[tex]y^2-16^2=h^2[/tex]
On the triangle with sides h,z,25 we have:
[tex]z^2-25^2=h^2[/tex]
Equating [tex]h^2[/tex]:
[tex]y^2-16^2=z^2-25^2\qquad\qquad [1][/tex]
On the bigger triangle with sides y,z,16+25=41 we have:
[tex]y^2+z^2=41^2[/tex]
Adding this last equation with [1]:
[tex]y^2-16^2+y^2+z^2=z^2-25^2+41^2[/tex]
Simplifying:
[tex]2y^2-16^2=41^2-25^2[/tex]
Operating:
[tex]2y^2-256=1681-625[/tex]
[tex]2y^2=1056-256[/tex]
[tex]2y^2=800[/tex]
Dividing by 2:
[tex]y^2=400[/tex]
Taking square root:
y=20
To enter the number in the required format:
[tex]\boxed{y=20\sqrt{1}}[/tex]
