
In the figure below, Calculate the length of PR.
Answer
490.2k+ views
Hint: To find the value of PR, we will first consider the . Since the triangle is a right-angled triangle, we will use the Pythagoras theorem. From this, we will get the side PS. Hence, . Now, consider triangle PRS and apply Pythagoras theorem. Through this, we will get side PR.
Complete step-by-step solution
We have to find the value of PR. It is given that . Hence the triangles PRS and PQS are right-angled triangles.
Let us first consider the . The sides PQ and QS are given. So we will use the Pythagoras theorem to find the side PS.
Pythagoras theorem states that the square of the largest side of a triangle will be equal to the sum of squares of the other two sides.
It is given that
Let us substitute these values in equation (i). We will get
We can write this as
Now, let us take the square root.
Now, let us consider the triangle PRS. We can apply Pythagoras theorem here.
It is given that
Hence,
Let us now substitute the values. We will get
Now, we can substitute these values in equation (ii).
We will get
Now let us solve this. We will get
Let us take the square root. We get
Hence, the value of .
Note: Pythagoras theorem must be thorough to solve these types of problems. Pythagoras theorem can be applied only when a triangle is a right-angled triangle. You may make an error in the Pythagoras theorem as . In the right-angle triangle, the largest side to be the hypotenuse.
Complete step-by-step solution

We have to find the value of PR. It is given that
Let us first consider the
Pythagoras theorem states that the square of the largest side of a triangle will be equal to the sum of squares of the other two sides.
It is given that
Let us substitute these values in equation (i). We will get
We can write this as
Now, let us take the square root.
Now, let us consider the triangle PRS. We can apply Pythagoras theorem here.
It is given that
Hence,
Let us now substitute the values. We will get
Now, we can substitute these values in equation (ii).
We will get
Now let us solve this. We will get
Let us take the square root. We get
Hence, the value of
Note: Pythagoras theorem must be thorough to solve these types of problems. Pythagoras theorem can be applied only when a triangle is a right-angled triangle. You may make an error in the Pythagoras theorem as
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