13. The sides of a triangle are 13 cm, 14 cm and 15 cm. The length of the shortest altitude is
(a) 12 cm
(1) 11.2 cm (c) 12.9 cm (d) 11.9 cm
14. The sides of a triangle are 17 cm, 25 cm and 26 cm. The length of the altitude to the longest
side correct up to two places of decimals is
(a) 16.32 cm
(b) 34.00 cm
(c) 15.69 cm
(d) 24.00 cm
15. The mean for counting numbers through 100 is
(a) 50
(b) 49.5
(c) 50.5
(d) 51
Answers
Answer:
option a
option c
option d
Step-by-step explanation:
Given : . The sides of a triangle are 13 cm, 14 cm and 15 cm.
To Find : The length of the shortest altitude
(a) 12 cm (b) 11.2 cm (c) 12.9 cm (d) 11.9 cm
Solution:
Triangle has three sides
13 , 14 , 15
s = (13 + 14 + 15)/2 = 21
Area of triangle using Heron formula
= √21(21-13)(21-14)(21-15)
= √21 * 8 * 7 * 6
= √7 * 3 * 2 * 2 * 2 * 7 * 2 * 3
= 7 * 3 * 2 * 2
= 84 cm²
Area of a triangle = (1/2) * base * height
shortest altitude will be on longest side 15 cm
Hence (1/2) * 15 * altitude = 84
=> altitude = 11.2 cm
Correct option is b) 11.2 cm
Similarly length of the altitude to the longest side in triangle with sides
17 cm, 25 cm and 26 cm is 15.69 cm
correct option is c) 15.69 cm
The mean for counting numbers through 100
Sum = 100(100 + 1)/2
Mean = (100 + 1)/2 = 50.5
Hence correct option is c) 50.5
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