untitled

In the above figure, let the base of two triangles be aandb respectively and their
height is h unit. If the areas of the triangle be Aand B square units, we can write,

b

a

bh

ah

B

A

2

1

2

1

orA:B a:b

i.e. ratio of two areas is equal to ratio of two bases.
Ordered proportional
By ordered proportional of a,b,c it is meant thata : b =b : c.
a,b,c will be ordered proportional if and only if b^2 =ac. In case of ordered
proportional, all the quantities are to be of same kinds. In this case, c is called third
proportional of a and band b is called mid-proportional of a and c.
Example 1. A and B traverses fixed distance in t 1 and t 2 minutes. Find the ratio of
average velocity of Aand B.
Solution : Let the average velocities of A and B be v 1 sec/metre and v 2 sec/metre
respectively. So, in time t 1 minutes A traverses v 1 t 1 metres and in t 2 minutes B
traverses the distance v 2 t 2 meters.

According to the problem, v 1 t 1 = v 2 t 2?

1

2

2

1

t

t

v

v

Here, ratio of the velocities is invers ely proportional to the ratio of time.
Activity: 1. Express 3.5 : 5.6 into 1 : a andb : 1

2. If x : y = 5 : 6, 3 x : 5y = What?

11 ˜3 Transformation of Ratio
Here, the quantities of ratios are positive numbers.
(1) If a:b c:dthenb:a d:c [Invertendo]

Proof : Given that,
d

c

b

a

?ad bc [multiplying both the sides by bd]

or,
ac

bc

ac

ad

[dividing both the sides by acwhere az 0 ,cz 0 ]

or,
a

b

c

d