Find the length of a side of a rhombus whose diagonals are 6cm and 8cm

In a rhombus, the diagonals intersect at a right angle and bisect each other. This means that the diagonals divide the rhombus into four congruent right triangles. Let's call the length of the side we are looking for "x". Using the Pythagorean theorem, we can find the length of each of the two right triangles that are formed by the diagonals: $$(\frac{6}{2})^2 + (\frac{8}{2})^2 = x^2$$ Simplifying this equation gives: $$9+16=x^2$$ Adding 9 and 16 gives us 25, so: $$25=x^2$$ To solve for x, we take the square root of both sides: $$\sqrt{25}=\sqrt{x^2}$$ Which simplifies to: $$5=x$$ Therefore, the length of the side of the rhombus is 5cm.