Question

How do you find the missing side of the right triangle given a = 5, b = 10?

Answer 1

Hint: Start the solution with writing the given part. Also since they have mentioned that the triangle whose third side is to be found is right angled, we can use the Pythagoras theorem. Write the formula for the Pythagoras theorem and substitute all the values. After solving the third side will be found.

Complete step-by-step answer:
We have been to two sides of the triangle and asked to find the third side using the given information. Also they have mentioned that the triangle is a right angled triangle which is the most important information required. As this tells us about the type the triangle is.
Since they have mentioned the triangle is right angled the easiest way to find the third side is using Pythagoras theorem.
\[{10^2} = {5^2} + {\text{sid}}{{\text{e}}^2}\]
 $ \Rightarrow 100 = 25 + {\text{sid}}{{\text{e}}^2} $
Solving further we get
 $
  100 - 25 = {\text{sid}}{{\text{e}}^2} \\
   \Rightarrow 75 = {\text{sid}}{{\text{e}}^2} \;
 $
Taking positive square root on both sides as we have to find side, we get
 $ {\text{side = }}\sqrt {75} $
Hence the required third side of a right angled triangle must have the value $ \sqrt {75} $ units respectively.
So, the correct answer is “ $ {\text{side = }}\sqrt {75} $ ”.

Note: The main part in the above question was that the triangle is a right angled triangle. If this was not mentioned, the methodology to solve the question would not have been the same as there are many different types of triangle whose methods of finding sides are different from one another.