+0  
 
+1
81
2
avatar

In the diagram below, angle PQR = angle PRQ = angle STR = angle TSR, RQ = 8, and SQ = \(2\).  Find PQ.

 

 Jan 21, 2022
 #1
avatar+514 
+4

Given the angles, we can conclude that triangles TSR ~ triangle TRQ ~ triangle RQP. 

Using base angles theorem, these 3 triangles are all isosceles, and QR = 8. That means QT = 8, and QS = 2 so ST = 6.

The ratio of QS / ST is also the ratio of PT / TR. Which is 1 : 3

 

Now after we have concluded the information above, we can set segment TR as \(x\)

Since we know there are similiar triangles, and we know TS = 6 and QR = 8, then we can say \({x\over6} = {8\over x}\)

Solving for x we get \(x = 4\sqrt{3}\). PT = one third of TR, so PT = \(4\sqrt{3}\over3\).

PQ = PT + PR.

 

Plugging in the values we get:

 

PQ = \(16\sqrt{3}\over3\)

 

 

gesmileymetry

 Jan 23, 2022
 #2
avatar
0

Hint:   RQ = TQ

 Jan 25, 2022

29 Online Users

avatar
avatar
avatar