Question

the ratio of base to height of a triangular field is 3:1.If the cost of cultivating field at ₹28 per sq.m is ₹9450,find its base and height

Answer 1

Let the height be a

Base = 3a

Cost of cultivating = Rs 9450.

Rate of cultivating = Rs 28 / m^2.

Area of field = Cost / Rate

Area of field = 9450 / 28


Base *Height /2 = 337.5 m^2

=> a * 3a = 675

=> 3a^2 = 675

=> a^2 = 225

=> a = 15 m

Height = 15 m

Base = 45 m

Answer 2

let x is included in the ratio.

base= 3x.
height=x.

area of field= 1/2× 3x ^2 (eq. 1)

area of field=total cost of cultivating/cost of cultivation of per square meter

=rs. 9,450/rs.28 m ^2

= 675/2m ^2 (eq.2)

eq. 1=eq.2

675/2m ^2= 1/2* 3x ^2

x ^2=225m ^2

x= 15m.

base= 3x= 3×15m=45m

height=x= 15m