What happens to a rectangle triangle if I divide per 2 a side length?

Question

Ok so I have a triangle ABC:

• Rectangle in the angle A

• BC = 49

And let's say:

• AB = y
• AC = x

That's the only values I have. Now, let's say I divide per 2 the AC value, what happens to the hypotenuse? And what is its new value?

Hope you can understand me, ask me if you need another information or clarification.

Answer 1

If by a rectangle you mean a right angle, then initially we have $$x^2+y^2=49^2 $$

If $AC$ is halved, then the new hypotenuse length becomes $$\sqrt{\left(\frac x2\right)^2 + y^2 } =\sqrt{ x^2 +y^2 +\frac{x^2}{4} -x^2 }=\sqrt{49^2 -\frac 34 x^2} $$

You’ll need the value of one of $x$ or $y$ to deduce the exact value.