Question 564960
Hi, suppose the altitude is CM, where M is such a point on AB.  Since triangle ABC is a right triangle, its area is equal to half the product of the lengths of the legs.  Also, if we rotate the triangle so that AB is the base, then the altitude CM will be the height in length.  So the area is AB*CM, but it is also equal to BC*AC.  So CM=BC*AC/AB.  Ok, but how do we find AB?  We use the Pythagorean Theorem:  AB^2=BC^2+AC^2, so AB=sqrt(7^2+24^2)=sqrt(49+576)=sqrt(625)=25.  So, CM=7*24/25=168/25=6.72