Question 2: CROP FIELD : A farmer has a field ABCD. Field ABCD is in the shape of rhombus and P, Q, R and S are the mid-points of the sides AB, BC, CD and DA respectively. The farmer wants to crop wheat in area PQRS and mustard crop in rest of the region.
Answers
Given : A farmer has a field ABCD. Field ABCD is in the shape of rhombus and P, Q, R and S are the mid-points of the sides AB, BC, CD and DA respectively. The farmer wants to crop wheat in area PQRS and mustard crop in rest of the region.
To Find : Ratio of crop
Solution:
ABCD is rhombus
in Δ ABD
P & S are mid points of AB & AD
Hence ΔAPS ≈ ΔABD & PS = BD/2
=> Area of ΔAPS = (1/2)² Area of ΔABD
=> Area of ΔAPS = (1/4) Area of ΔABD
Similarly Area of ΔCQR = (1/4) Area of ΔCBD
Area of ΔABD + Area of ΔCBD = Area of ΔABCD
Area of ΔAPS + Area of ΔCQR = (1/4) Area of ΔABCD
Similarly
Area of ΔBPQ + Area of ΔDRS = (1/4) Area of ΔABCD
Area of ΔAPS + Area of ΔCQR + Area of ΔBPQ + Area of ΔDRS = (1/4) Area of ΔABCD + (1/4) Area of ΔABCD
=> Area of ΔAPS + Area of ΔCQR + Area of ΔBPQ + Area of ΔDRS =
= (1/2) Area of ΔABCD
area PQRS = Area of ΔABCD -(1/2) Area of ΔABCD
=> area PQRS = (1/2) Area of ΔABCD
Area of wheat Crop = Area of mustard Crop
=> Area of wheat Crop : Area of mustard Crop = 1 : 1
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