=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.

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

Understanding/ analysing the given problem
1. Identifying/ Naming the triangles
2. Identifying the sides whose lemgth 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)
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
       x = 15 cms