Area of Similar Figures

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This item is taken from IGCSE Mathematics (0580) Paper 41 of May/June 2013.


To deal with this item, let us summarize the details of the problem:
   (a) Syllabus area: Mensuration
   (b) Specific topic: Area of Similar Figures

   (c) Formula Needed:

IGCSE,mathematics,Cambridge,examination,triangles,similarity,polygon,areas,correspondence,geometry,mensuration,proportion,past papers,revisions
IGCSE,mathematics,Cambridge,examination,triangles,similarity,polygon,areas,correspondence,geometry,mensuration,proportion,past papers,revisions
Let us first determine the given in the problem.
IGCSE,mathematics,Cambridge,examination,triangles,similarity,polygon,areas,correspondence,geometry,mensuration,proportion,past papers,revisions
Using the relation of the areas and corresponding lengths of similar figures, 
IGCSE,mathematics,Cambridge,examination,triangles,similarity,polygon,areas,correspondence,geometry,mensuration,proportion,past papers,revisions
Cross multiply:
IGCSE,mathematics,Cambridge,examination,triangles,similarity,polygon,areas,correspondence,geometry,mensuration,proportion,past papers,revisions
Simplify then calculate the value of l by getting the square root:
IGCSE,mathematics,Cambridge,examination,triangles,similarity,polygon,areas,correspondence,geometry,mensuration,proportion,past papers,revisions
Another way is to directly get the square root of both sides to eliminate the exponent/power.
IGCSE,mathematics,Cambridge,examination,triangles,similarity,polygon,areas,correspondence,geometry,mensuration,proportion,past papers,revisions
Then manipulate the equation to get the value of l.
IGCSE,mathematics,Cambridge,examination,triangles,similarity,polygon,areas,correspondence,geometry,mensuration,proportion,past papers,revisions
Therefore, the length (l) of the base of the first figure is 5.75 cm.

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