In the figure above, angles QPA and BAP are right, PQ = 3, AB = 5 and

Question

https://gmatclub.com/forum/download/file.php?id=54280 In the figure above, angles QPA and BAP are right, PQ = 3, AB = 5 and AP = 8. If N is an intersection of BP and AQ, then what is the length of the perpendicular NM? A. 5/8 B. 1 C. 15/8 D. 2 E. 5/2 Project PS Butler Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS Are You Up For the Challenge: 700 Level Questions Untitled.png

GMATinsight · Accepted Answer

Strategy :
- Find two pairs of Similar Triangles
- Use the ratio of the corresponding sides

Answer: Option C

Please find the solution as attached.

https://www.youtube.com/watch?v=vRUGyCuFmy0

kris19 · Answer

Given: PQ = 3, AB = 5 and AP = 8
then what is the length of the perpendicular NM?
Assume NM = h, PM = x, and MA = y, so that x+y = 8
  Projection of N on line AB is N', so AN' = h, and N'B = 5-h  
Now, angle BNN' = angle NPM
 \frac{(5-h)}{y }= \frac{h}{x}  ----- (1)
solving (1), we get  h = \frac{5x}{8} 
  Again, projection of N on line PQ is N'', so PN'' = h, and N''Q = 3-h  
Now, angle QAP = angle QNN''
 \frac{3}{8} = \frac{(3-h)}{x}  ---- (2)
substituting 'h' (1) in (2), and solving (2) for x, we get x = 3,
finally h = NM = 15/8

Kinshook · Answer

Given: 1. In the figure above, angles QPA and BAP are right 2. PQ = 3, AB = 5 and AP = 8. 3. N is an intersection of BP and AQ Asked: What is the length of the perpendicular NM? Screenshot 2020-05-06 at 9.04.46 AM.png Triangles PNM & PBA are similar x/y = 5/8; y = 8x/5 (1) Triangles ANM & AQP are similar (8-y)/x = 8/3 8-y = 8x/3 (2) (1) + (2) 8-y + y = 8 = 8x/5 + 8x/3 = 8*(5+3)x/15 = 64x/15; x = 8*15/64 = 15/8 IMO C

bumpbot · Answer

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In the figure above, angles QPA and BAP are right, PQ = 3, AB = 5 and

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In the figure above, angles QPA and BAP are right, PQ = 3, AB = 5 and

Prep Toolkit

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