a farmer has right angles triangular field of sides 72m,120mand 96m.he wants to divide the field into two parts ,by joining any two points in two of its smaller sides such that the samller sides are divided in the ration of 5:3,so that he can plant smaplings of tomato in the bigger region and that of mangoes in the other region .in the figure ab =72m and ac=96m and bc=120m and de are the pints on the sides ab and ac , a)the ratio of the area of smaller region to bigger region of the field formed is i)25;9 ii)9:25 iii)25:39 iv)none of the above b)the length of the largest side of the part in which samplings of mangoes are planted is i)75m ii)84m iii)60m iv)96m c) the ratio of the perimeter of the samller region to bigger region of the field formes if i)5:3 ii)3:5 iii)5:8 iv)none of these
Answers
Given : a farmer has right angled triangular field of side 72 m, 120m,96m.sides are divided in the ratio 5 : 3,
plant saplings of tomato in the bigger reason and that of mango in other reason
To Find : Area of the complete field
Area of tomato sapling
Area of Mango sapling
Solution:
right angled triangular field of side 72 m, 120m,96m.sides
Area of triangle = (1/2)72*96
= 3456 sq m
Area of complete field = 3456 m²
sides are divided in the ratio 5 : 3,
=> AD = (5/(5 + 3)) 72 = 45
AE =(5/(5 + 3))96 = 60
Area of ΔADE = (1/2) * 45 * 60 = 1350 m²
Area of BCED = 3456 - 1350 = 2106 m²
Area of tomato = 2106 m²
Area of Mango = 1350 m²
Largest side in which mango is there = √45² + 60² = 75 m
perimeter ADE = 45 + 60 + 75 = 180
perimeter ABC = 72 + 96 + 120 = 288
180 : 288
= 5 : 8
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