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Two Ladders

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2


The picture shows two ladders propped against facing walls. The end of the first ladder is $5\text{m}$ above the base of the second wall. The second ladder is $5\text{m}$ above the base of the first wall.
 

Can you work out at what height the ladders cross?

Are you surprised that we don't need to know the distance between the two walls?


 


Suppose now the first ladder is $10 \text{m}$ above the base of the second wall, with the second ladder remaining as before.

Can you work out at what height the ladders cross now?

Click below to reveal a diagram that may help you get started:
 

Can you find any pairs of similar triangles in this diagram?
How do these help you to find the value of $x$?
 
 
 

Suppose the first ladder meets the wall at a height of $a$ metres, as in the diagram below.
 

At what height do the ladders cross now?


Suppose the second ladder meets the wall at a height of $b$ metres, as in the diagram below.
 

At what height do the ladders cross now?