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In rectangle ABCD points P and Q lie on AB and DC respectively. Angle PMQ is a right angle, M is the midpoint of BC and PB = 4/3BC. What is the ratio PM:MQ? Express your answer as a common fraction.

 

 

 Nov 27, 2019
 #1
avatar+19 
+1

Let's see...

The answer is 8/3.

 

so

and 90-

Additionally,

 

Therefore,

 

Also,

 

So, 

Triangle PBM ~Triangle MCQ.

BC=MC*2 because M is the midpoint of line BC.

PB= (4/3)BC= (8/3)MC.

Because Triangle PBM and Triangle MCQ are similar, we can assume that PM/MQ=PB/MC=1/(8/3)=8/3.

Hope this helped! 🧭

 Nov 27, 2019
edited by artsyleilani  Nov 27, 2019
 #2
avatar+212 
+2

Oh! Thanks! I understand your train of thought

 Nov 27, 2019
 #3
avatar+2505 
+2

Also, what I did was trying to draw a new point (x) on AD in such that PMQX is a rectangle.

 Nov 27, 2019

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