Question

the base of a triangular field is three times of its altitude. If the cost of levelling the field at rupees 25 per hectare is rupees 33 7.50, find its base and corresponding altitude​

Answer 1

Rate of levelling=₹25 / hectare

total cost of levelling =337.50

land in hectare=total cost /rate

= 337.25/25

= 13.49 hectare

as we know that 1 hectare is equal to10000 m²

so area of field = land in hectare x. 10000

= 13.49 x 10000

= 134900 m²

let altitude of field be @

then base will be 3@

area of triangle = 1/2 base x hight

134900= 1/2 x 3@ x @

134900 x 2 = 3 @²

134900 x 2 / 3 = @²

89,933.34 = @²

@ = 300 (approx)
altitude is 300 m

Answer 2

Answer:

let the altitude of the triangle be x

Hence base = 3x

Area of triangle = (1/2) × base × height

= (1/2) × (x) × (3x) = 3x^2/2

Cost of sowing the field at rs 25 per hectare = 25 × 3x^2/2 = 75x^2/2

Therefore,  75x^2/2= 3375/10

=>x=3

Base = 3(3) = 9

Hence base is 9 and altitude is 3.

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