Question

A rhombus with area $840$ has a diagonal of length $40$. what is its side length?

Answer 1

The area of a rhombus is half the product of its diagonals, so the missing diagonal is equal to (2*840)/40 = 42.

we also know that the 2 diagonals bisect the rhombus into 4 identical right triangles.
the legs of the right triangle are equal to half of the diagonals, which in this case are 20 and 21(40/2 & 42/2)

then we can use the Pythagorean theorem to solve for the side length, and get 29    :)