Question:
In triangle PQR, PM is perpendicular to QR. If ‘T’ is a point in between ‘Q’ and ‘M’ such that PT = \(5\sqrt3\) cm, PM = \(\sqrt{39}\) cm then find the value of PQ such that QM : TM = 5 : 2.
In triangle PQR, PM is perpendicular to QR. If ‘T’ is a point in between ‘Q’ and ‘M’ such that PT = \(5\sqrt3\) cm, PM = \(\sqrt{39}\) cm then find the value of PQ such that QM : TM = 5 : 2.
Updated On: Sep 10, 2024
- \(3\sqrt{70}\) cm
- \(5\sqrt{35}\) cm
- \(2\sqrt{66}\) cm
- \(3\sqrt{45}\) cm
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The Correct Option is C
Solution and Explanation
According to the question,
Given, PT = \(5\sqrt3\) cm and PM = \(\sqrt{39}\) cm
In triangle PMT, using Pythagoras theorem
TM2 = PT2 - PM2
Or, TM2 = (\(5\sqrt3\))2 - (\(\sqrt{39}\))2
Or, TM2 = 75 - 39 = 36
Or, TM = 6 cm
Therefore, QM = 6 × (5/2) = 15 cm
In triangle PMQ, using Pythagoras theorem
PQ2 = PM2 + QM2
Or, PQ2 = (\(\sqrt{39}\))2 + (15)2
Or, PQ2 = 39 + 225 = 264
Or, PQ = \(2\sqrt{66}\) cm
So, the correct option is (C) : \(2\sqrt{66}\) cm.
Given, PT = \(5\sqrt3\) cm and PM = \(\sqrt{39}\) cm
In triangle PMT, using Pythagoras theorem
TM2 = PT2 - PM2
Or, TM2 = (\(5\sqrt3\))2 - (\(\sqrt{39}\))2
Or, TM2 = 75 - 39 = 36
Or, TM = 6 cm
Therefore, QM = 6 × (5/2) = 15 cm
In triangle PMQ, using Pythagoras theorem
PQ2 = PM2 + QM2
Or, PQ2 = (\(\sqrt{39}\))2 + (15)2
Or, PQ2 = 39 + 225 = 264
Or, PQ = \(2\sqrt{66}\) cm
So, the correct option is (C) : \(2\sqrt{66}\) cm.
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