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Question
In the figure: ∠PSQ = 90o, PQ = 10 cm, QS = 6 cm and RQ = 9 cm. Calculate the length of PR.
Solution
Pythagoras theorem states that in a right-angled triangle, the square on the hypotenuse is equal to the sum of the squares on the remaining two sides.
First, we consider the ΔPQS and applying Pythagoras theorem we get,
PQ2 = PS2 + QS2
102 = PS2 + 62
PS2 = 100 - 36
PS = 8
Now, we consider the ΔPRS and applying Pythagoras theorem we get,
PR2 = RS2 + PS2
PR2 = 152 + 82
PR = 17
The length of PR 17 cm.
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