Page 114 - ICSE Math 6

11. The angles of a triangle are in the ratio 1 : 7 : 2. Also, the sum of the angles of a triangle is 180º.
Find the angles of the given triangle.
12. A rope of length 3 m 20 cm is cut into two pieces such that the ratio of the lengths of the pieces
is 7 : 9. Find the length of the larger piece (in cm).
13. Compare the following ratios.

(a) 5 : 8 and 7 : 9 (b) 11 : 15 and 13 : 14 (c) 7 : 18 and 14 : 36
(d) 16 : 19 and 21 : 23 (e) 15 : 32 and 9 : 17 (f) 8 : 15 and 7 : 16

Proportion
When two ratios are equal, they are said to be in proportion. If p, q, r and s are such that
p : q = r : s, then we say that p, q, r and s are in proportion. The numbers used in proportion are
called its terms, where p is the first term, q is the second term, r is the third term and s is the
fourth term. Also, the first and fourth terms are known as extreme terms and the second and third
terms are known as mean terms. Proportion is denoted by the symbol ‘: :’ and is read as ‘p is to
q as r is to s’. It is not necessary that all the four quantities forming
a proportion are of the same kind. The first two quantities must be Maths Info
of the same kind and the last two quantities must be of the same Product of extremes = Product
kind. For example, 3 m, 5 m, 18 s and 30 s are in proportion because of means.
3 : 5 = 18 : 30.

Example 10: Check whether the two ratios form a proportion or not.
(a) 1 : 7 and 5 : 7 (b) 15 : 24 and 10 : 16
1 5
Solution: (a) Since, 1 : 7 = and 5 : 7 =
7 7
1 : 7 ≠ 5 : 7 and hence they do not form a proportion.
5 15 5 5 10 5
(b) Since, 15 : 24 = = and 10 : 16 = =
24 8 8 16 8 8
15 : 24 = 10 : 16 and hence they form a proportion.
Example 11: The numbers 7, 33, x and 66 are in proportion. Find x.

Solution: The numbers, 7, 33, x and 66 are Alternatively,
in proportion, i.e., 7 : 33 = x : 66. Product of extremes = Product of means
⇒ 7 = x 7 × 66 = 33 × x
33 66
7× 66 2 7× 66 2
⇒ x = = 14 ⇒ x = = 14
33 33

EXERCISE 8.2

1. Write True or False.
(a) 6 : 9 : : 10 : 15 (b) 11 : 22 : : 7 : 14

(c) 2 : 67 : : 13 : 39 (d) 5 : 50 : : 1 : 11
(e) 5 kg : 10 kg = 15 km : 30 km (f) 13 mm : 39 mm = 3 s : 8 s
(g) 2 L : 7 L = ` 10 : ` 35 (h) 3 hours : 12 hours = 1 s : 5 s

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