John had a farm with many animals like cows, dogs, horses etc. He had sufficient
grass land for the cows and horses to graze, One day Three of his horses were tied
with 7metre long ropes at the three corners of a triangular lawn having sides 20m,
34m and 42m.
27. Area of the triangular lawn is
(a) 326 m2
(b) 336 m2
(c) 306 m2
(d) 316 m2
28. Find the area of the field that can be grazed by the horses
(a) 326 m2
(b) 44m2
(c) 306 m2
(d) 77m2
29. The cost of fencing the triangular lawn at the rate of Rs 30 per metre, is
(a) Rs 2880
(b) Rs 2590
(c) Rs 10080
(d) Rs 3360
30. John had a beautiful garden in the form of a quadrant of radius 7m asshown, He
wanted to fence it to protect the flowers. Find the length of wirerequired to fence
it completely.
(a) 11m
(b) 18m
(c) 25m
(d) 36 m
Answers
Given : Three of his horses were tied with 7metre long ropes at the three corners of a triangular lawn having sides 20m, 34m and 42m.
To Find : Area of the triangular lawn
area of the field that can be grazed by the horses
The cost of fencing the triangular lawn at the rate of Rs 30 per metre
Solution:
sides 20m, 34m and 42m.
s = (20 + 34 + 42)/2
= (96/2)
= 48 m
Area of triangle = √s(s-a)(s-b)(s-c)
= √48(48-20)(48-34)(48-42)
=√48 (28)(14)(6)
= √2* 2 * 2 * 6 * 14 *2 * 14 * 6
= 2 * 2 * 6 * 14
= 336 m²
area of the field that can be grazed by the horses
Sum of angle of a triangle = 180°
= (180/360)πr²
= (1/2) (22/7)7²
= 11 * 7
= 77 m²
Perimeter of triangle = 20 + 34 + 42 = 96
cost of Fencing = 96 * 30 = 2880 Rs
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