The figure below shows a triangular lawn labeled PQR. There are two fences, AB and BC.

What is the total length of the fence AB and BC?

Question

The figure below shows a triangular lawn labeled PQR. There are two fences, AB and BC.
 

 
What is the total length of the fence AB and BC?

anonymous · Answer

attachment

anonymous · Answer

@kgiddens

ujjwal · Answer

I can see two sets of similar triangles 
a) $\Delta$PAB and $\Delta$PRQ
b) $\Delta$QBC and $\Delta$QPR

Now use the property of similar triangles to find the required lengths.
In similar triangles corresponding sides are proportional.

cwrw238 · Answer

use the theorem that a line parallel to base of triangle divides the other 2 lines in same ratio
let AP = x  and AR = y
PB = 40 - 24 = 16
so we get following equations

x + y = 50
x/y = 16/24  = 2/3
solve for x and y

cwrw238 · Answer

y will = BC as they are opposite angles of parallelogram
also AB / 80  = 2 /3
solve for AB

cwrw238 · Answer

00ops  - sorry:
because triangles are similar
AB/ 80 = 2 / 5