Question

the base of a triangular field is twice its altitude. if the cost of levelling the field,at the rate of Rs 10 per m2 is Rs 4000,find its base and altitude

Answer 1

thecost of level = 10 rs
the land be level = 4000/10
=400 m^2
let altitude be = x
let base be = 2x
The Area of triangle = 1/2*b*H
400=1/2*2x*x
800=2x^2
400=x^2
sq. root 400= x
20 = x


base = 2x = 2*20= 40m
Altitude= x = 20 m

Answer 2

x is 20, 2x is 40

Rate / m² is ₹10

so, area of the triangle = total rate/ rate per metre

so, 4000/10 = 400 m² is the area

Now,

let altitude be x

base is twice of x which is 2x

area of triangle (formula) = ½b×h

= ½ x×2x = 2x²/2 =400

2x²= 400×2 =800

x²= 800/2 = 400

therefore,

x =

$\sqrt{400}$

which is 20

so x is 20 and 2x = 40

.