Question

C. In the figure PSQ = 90°, PQ = 10 cm, QS = 6cm and RQ = 9cm. Calculate the
length of Pr​

Answer 1

Consider the ∆PRS:-

$\huge\blue{♚Solution♚}$

✦ Pythagoras theorem states that in a right-angled triangle, the square on the hypotenuse is equal to the sum of the sum of the squares on the remaining two sides.

✯ First, we consider the ∆PQS and applying Pythagoras theorem we get,

$\orange{➫\:PQ²\:=\:PS²\:+\:QS²}$

$\orange{➫\:10²\:=\:PS²\:+\:6²}$

$\orange{➫\:PS²\:=\:100\:–\:36}$

$\orange{➫\:PS\:=\:√64}$

$\orange{➫\:PS\:=\:8}$

✮ Now, we consider the ∆PRS and applying Pythagoras theorem we get,

$\red{➬\:PR²\:=\:RS²\:+\:PS²}$

$\red{➬\:PR²\:=\:15²\:+\:8²}$

$\red{➬\:PR²\:=\:225\:+\:64}$

$\red{➬\:PR\:=\:√289}$

$\red{➬\:PR\:=\:17}$

✯ Hence, The length of PR is 17 cm

$\huge\green{❥Hope \: it \: Helps࿐}$