Question 1131574
.
<pre>
The triangle is a right angled triangle with the right angle at B.


The simplest way to check it is this:

    {{{abs(AC)^2 - abs(BC)^2}}} = {{{25^2-24^2}}} = (25-24)*(25+24) = 1*49 = 49 = {{{7^2}}} = {{{abs(AB)^2}}}.


Let H be the distance under the question. Notice that H is nothing else as the altitude of the triangle ABC drawn from 
the right angle vertex B to the hypotenuse AC.


Then we have two expressions for the triangle area 

    Area = {{{(1/2)*abs(AB)*abs(BC)}}} = {{{(1/2)*abs(AC)*H}}}.


It gives  H = {{{(7*24)/25}}}.     <U>ANSWER</U>
</pre>

Solved.


-----------------


It is how this problem has to be solved.