A side of a triangular field is 2.5 times its corresponding altitude.The cost of levelling the field at rate of rupees 52 per square m is rupees 31460.Find the length of the side and its corresponding altitude.
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1)given
cost of leveling 1 sq m field = Rs 52
area of the field levelled with Rs 31460 = 31460/52 = 605 sq m---(1)
2)let the altitude of the triangle = x m
length of the corresponding side = 2.5x m
area of the triangle = (altitude * corresponding height)/2
=( x * 2.5x) /2sq m ---(2)
(2) = (1)
(x* 2.5x) /2= 605
x²= (2*605)/2.5
x² = (2*605*10)/25
x² = 2*121*2
x² = 484
x²= (22)²
x = 22 or -22
x should not be negative
therefore x= 22
now
altitude = x = 22 m
corresponding side = 2.5x = 2.5 *22 =55m
cost of leveling 1 sq m field = Rs 52
area of the field levelled with Rs 31460 = 31460/52 = 605 sq m---(1)
2)let the altitude of the triangle = x m
length of the corresponding side = 2.5x m
area of the triangle = (altitude * corresponding height)/2
=( x * 2.5x) /2sq m ---(2)
(2) = (1)
(x* 2.5x) /2= 605
x²= (2*605)/2.5
x² = (2*605*10)/25
x² = 2*121*2
x² = 484
x²= (22)²
x = 22 or -22
x should not be negative
therefore x= 22
now
altitude = x = 22 m
corresponding side = 2.5x = 2.5 *22 =55m
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