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

Question

asked Dec 8, 2021 213k views

1 Answer

Questzen · Answer 1 · 2021-12-13T05:02:07+0000

Answer:

y=20√(1)

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:

$\boxed{y=20√(1)}$