Question

CAN SOMEONE PLEASE HELP ME WITH THIS GEOMETRY QUESTION THANK YOU !!!

Answer 1

Answer:

$y=20\sqrt{1}$

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:

$y^2-16^2=h^2$

On the triangle with sides h,z,25 we have:

$z^2-25^2=h^2$

Equating $h^2$:

$y^2-16^2=z^2-25^2\qquad\qquad [1]$

On the bigger triangle with sides y,z,16+25=41 we have:

$y^2+z^2=41^2$

Adding this last equation with [1]:

$y^2-16^2+y^2+z^2=z^2-25^2+41^2$

Simplifying:

$2y^2-16^2=41^2-25^2$

Operating:

$2y^2-256=1681-625$

$2y^2=1056-256$

$2y^2=800$

Dividing by 2:

$y^2=400$

Taking square root:

y=20

To enter the number in the required format:

$\boxed{y=20\sqrt{1}}$