Let's look at an example , which will help us to understand what ratio and proportion
Consider any polygon, say a rectangle.
Let the dimensions of a rectangular board be 50 cm and 20 cm.
$\Rightarrow$ l = 50 cm, b = 20 cm.
Let each of the dimensions be increased in the ratio 2:3.
If the increased length = x cm, then $\frac{50}{x}=\frac{2}{3}$
$\therefore$ x = 75
$\therefore$ The increased length of the rectangular board = 75 cm.
In the same way, the increased breadth of the rectangular board = 20x $\frac{3}{2}$
= 30 cm
We find that a ratio and proportion can be used to change the dimensions of a figure, such that the figure retains its shape. We get 2 similar rectangles. Hence, we get 2 equal ratios.
Ratios of length : breadth are equal.
$\frac{50}{20} =\frac{75}{30}$ (each = $\frac {5}{2}$)
or, ratio of lengths = ratio of breadths
$\frac{75}{50} =\frac{30}{20}$ (each = $\frac {5}{2}$)
From these equal ratios, we get 4 quantities in math proportion.
50, 20, 75, 30 are in proportion.
70, 50, 30, 20 are in proportion.
Thus, ratio and proportion form the basis of similarity of figures.
Concept of Similarity
All pairs of objects in ratio and proportion , which have the same shape, but differ in size, are said to be similar.
Observe the following pairs of similar figures.
Important Points in Solving Ratio and Proportion
In ratio and proportion ,Two polygons having the same number of sides are similar if and only if:
- The angles of one polygon are equal to the corresponding angles of the other.
- The sides of one polygon are proportional to the corresponding sides of the other.
- The ratio of the corresponding sides of similar polygons also equals
- the ratio of their perimeters
- the math ratio of the lengths of the diagonals.
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