ΔPQR is right angled at Q such that PQ = (x - y), QR = x, and PR = (x + y). S is a point on QR such that QS = PQ,The ratio QS ∶ SR for any values of x and y is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 3 : 1.
We consider a triplet (3, 4, 5)
By the Pyrhogoreous theorem, we know that the measure of hypotenuse in ΔPQR will be the greatest.
So, PR = 5
It is given that
⇒ PQ = (x - y), QR = x, PR = (x + y)
It is obvious from the question that, QR is greater than PQ
So, QR = 4
and, PQ = 3
Given that
⇒ QS = PQ
Then,
⇒ QS = PQ = 3
And if QS = 3 then, SR = 4 - 3 = 1
Thus, QS : SR = 3 : 1