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In the figure below, PSR=90,PQ=10cm,QS=6cm and RQ=9cm. Calculate the length of PR.

Answer
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Hint: To find the value of PR, we will first consider the ΔPQS . Since the triangle is a right-angled triangle, we will use the Pythagoras theorem. From this, we will get the side PS. Hence, RS=RQ+QS . Now, consider triangle PRS and apply Pythagoras theorem. Through this, we will get side PR.

Complete step-by-step solution
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We have to find the value of PR. It is given that PSR=90 . Hence the triangles PRS and PQS are right-angled triangles.
Let us first consider the ΔPQS. 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.
PQ2=PS2+QS2...(i)
It is given that PQ=10cm,QS=6cm 
Let us substitute these values in equation (i). We will get
102=PS2+62
We can write this as
PS2=10036=64
Now, let us take the square root.
PS=8cm
Now, let us consider the triangle PRS. We can apply Pythagoras theorem here.
PR2=RS2+PS2...(ii)
It is given that QS=6cm and RQ=9cm.
Hence, RS=RQ+QS
Let us now substitute the values. We will get
RS=6+9=15cm
Now, we can substitute these values in equation (ii).
We will get
PR2=152+82
Now let us solve this. We will get
PR2=225+64=289
Let us take the square root. We get
PR=17cm
Hence, the value of PR=17cm.

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 PQ2=PS2QS2. In the right-angle triangle, the largest side to be the hypotenuse.
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