Answer: The third side x = 8cm
Step-by-step explanation: With two sides given as 10cm and 6cm, and no angle provided, we shall apply the Pythagoras theorem in order to find the value of the third side. We are taking this step, based on the fact that the Pythagoras theorem does not depend on the availability of any of the angles, as long as two of the sides are known. It’s equally important that we remember this theorem only applies to right angled triangles. The theorem states thus;
AC^2 = AB^2 + BC^2
Where AC is the hypotenuse (the longest side), and AB and BC are the other two sides.
Assuming that the longest side is 10, our formula would become
10^2 = 6^2 + BC^2
100 = 36 + BC^2
Subtract 36 from both sides of the equation
64 = BC^2
Add the square root sign to both sides of the equation
8 = BC
Therefore the third side in the triangle is 8cm