Ratio and Proportion

ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ

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1. Cabinet of mathematical curiosities - Ian Stewart
2. Cabinet of mathematical curiosities - Ian Stewart

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=Ratio and Proportionality

Exercise 2.4.2

In the adjacent figure, two triangles are similar. Find the length of the missing side This problem can be solved with the following steps.

1. Prerequisites: students should know the concept of similarity and proportionality

*Proportionality : two ratios are equal then four quantities are in proportional

               *Similar Triangles : If two triangles are said to be similar 1. if they are equiangular 2. the corresponding side are proportional

1. Understanding/ analysing the given problem
   1. Identifying/ Naming the triangles
   2. Identifying the sides whose length is not given
   3. comparing two sides of triangles (visualising that 1st triangle is smaller than 2 nd triagle and viceversa
   4. should identify the corresponding sides (sides having same allignment)
2. Procedure
   1. find the ratio between the corresponding sides whose length is known $13/39=13*1/13*3=1/3$
   2. express proportional corresponding sides (using the property of similarity)

   AC/DF = AB/DE

13/39 = 5/x 13 : 39 = 5 : x (use the property of proportionality i.e Product of extremes is equal to product of means) 13 * x = 39 * 5

       x = 39* 5 /13

Use the following Geogebra applet to understand proportion

Math Fun

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