510 /www/nrich/html/content/97/06/six1/ 1 2011-02-01T00:00:01 <mdoxml version="1.0"><br></br> <mdo:image border="0" align="texttop" alt="" src="ladders.gif"></mdo:image> <br></br> <p>Two ladders are propped up against facing walls as shown in the diagram. The end of the first ladder is 10 metres above the foot of the first wall. The end of the second ladder is 5 metres above the foot of the second wall. At what height do the ladders cross?</p> <p>Can you say other circumstances in which the ladders cross at a height which is one third and two thirds of the heights up the walls respectively?</p> <p>Can you generalise this result for ladders at different heights?</p> <br></br></mdoxml> <mdoxml version="1.0"> <mdo:image src="lads.gif" align="texttop" border="0" alt=""></mdo:image> <br></br> <p>Triangles ABC and CDE are similar and the ratio of DE:AB is 2:1,<br></br> so the ratio CN:CM must also be 2:1.<br></br> Since NM = DE =10m,<br></br> CM = 3 1/3 metres</p> <p>The ladders cross at a height of 3 1/3 metres.</p> </mdoxml> <mdoxml version="1.0"><p>Possible extension: <a href="/298">Two Trees</a></p></mdoxml> 2 4 0 0 0 1 0 Two ladders are propped up against facing walls. The end of the first ladder is 10 metres above the foot of the first wall. The end of the second ladder is 5 metres above the foot of the second wall. At what height do the ladders cross? Transformations and their Properties Similarity Fractions, Decimals, Percentages, Ratio and Proportion Calculating with ratio & proportion Admin Short problems Information and Communications Technology smartphone