Question 1131574
Draw your description.  Including altitude from B to AC you can call the left segment along AC as x and the right segment along AC as  25-x.  Let y be the length of the altitude.



Just a start:
{{{system(x^2+y^2=7^2,(25-x)^2+y^2=24^2)}}}


Solve for the value of y.


If substitute for y^2, then ....   {{{x=49/25}}}.


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{{{highlight(y=7*24/25)}}}