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.

• A. $3\sqrt{70}$ cm
• B. $5\sqrt{35}$ cm
• C. $2\sqrt{66}$ cm
• D. $3\sqrt{45}$ cm

Answer 1

Answer: (C)

$2\sqrt{66}$ cm

Answer 2

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.