Geometric Ratios

When two objects are similar, the geometric ratio of the lengths of a pair of corresponding sides is the same as the ratio of any other pair of corresponding linear measurements of the two objects.it is called as geometric ratios.

Therefore:

1)   Lengths of corresponding sides are equal.

2)   The ratio of the lengths of any pair of corresponding sides is the same as the ration of corresponding perimeters, altitudes, or medians in.

 

Definition of geometric ratios:

 

Geometric ratios of two numbers x and y is the division `(x)/(y)` . The results of examination or measurement often must be compared with some standard value in order to have any meaning. For example, to say that a man can read 800 words per minute has little meaning as it stands.

However, when his rate is compared to the 350 words per minute of the average reader, one can see that he reader. How mach faster? To find out, his average rate of reader speed, as follows:

600 / 350 =  12 / 7

Thus, for  every 7 word read by the average reader, this man reads 12.One of the way of making this comparison is to say that he reads 1 `(5)/(7)`  times as fast as the average reader.

When the relationship between two numbers is shown in this way, they are compared as a ratio in geometry. Geometric ratios are an evaluation of two like quantities. It is the quotients get by simplifying the first number of a comparison by the second in geometry.

 

Example for geometric ratios:

 

A 50-inch segment is divided into three parts, lengths have the ratio 1 : 3 : 7. What is the length of the longest part in geometric ratios?


Solution:

Let measure of Shortest piece = 1x

Measure of middle piece     = 3x

Measure of longest piece  = 7x

1x + 3x + 7x  = 50

11x =50

 x= 50 / 11 = 4.54

Shortest piece:

1x = 1(4.54) = 4.54

Middle piece :

3x = 3(4.54) = 13.62

Longest piece :

          7x = 7(4.54) = 31.78 

The longest part has a measure of 31.78 inches.