Question 606387
Your assumptions are good so far!
Now drop a line from the vertex L perpendicular to the base (KM)at point Q.  This will bisect KM at Q and you will have two congruent right triangles KLQ and MLQ.
The hypotenuse of these right triangles is 35cm and the base of one of the right triangles is {{{42/2 = 21}}}.
Now you can use the Pythgorean theorem to find the height (h).
{{{(35)^2 = (21)^2+h^2}}}
{{{1225 = 441+h^2}}} Subtract 441 from both sides.
{{{784 = h^2}}} Take the square root of both sides.
{{{h = 28}}}