A farmer has triangular field of sides 72m, 120m and 96m. He want to divide the field into two parts, joining any two points on two of its smaller sides such that the smaller sides are divided in the ratio of 5:3 so that he can plant samplings of tomato in the bigger region and that of mango in the other region
(ii) The area of part, where samplings of tomatoes are planted, is
(a) 2106 m2
(b) 2160 m2
(c) 1728 m2
(d) none of these
Answers
Given : A farmer has triangular field of sides 72m, 120m and 96m.
divide the field into two parts, joining any two points on two of its smaller sides such that the smaller sides are divided in the ratio of 5:3 so that he can plant samplings of tomato in the bigger region and that of mango in the other region
To Find : The area of part, where samplings of tomatoes are planted
(a) 2106 m2
(b) 2160 m2
(c) 1728 m2
(d) none of these
Solution:
triangular field of sides 72m, 120m and 96m.
s = (72 + 120 + 96)/2 = 144 m
Area = √s(s - a)(s - b)(s - c)
= √144(144 - 72)(144 - 96)(144 - 120)
= √12²(72)(48)(24)
= √12²(24*3)(4²*3)(24)
= 12 * 24 * 3 * 4
= 3,456 m²
smaller sides are divided in the ratio of 5:3
Area of larger region = (5/(5 + 3)) * 3456
= 5 (432)
= 2160 m²
The area of part, where samplings of tomatoes are planted 2160 m²
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