Question

The base of a triangular field is three times its altitude. If the cost of levelling the field at ₹ 30.50 per sq .metre is ₹ 7350, find its base and height.

Answer 1

We know the area of a triangle = $\frac{1}{2}$ x (base) x (altitude)
Let the altitude of the triangle = a
therefore, base length = 3a
=> area, A = $\frac{1}{2}$ x 3a x a
=> $A = \frac{3}{2} a^{2}$ sq.metre

Price of levelling the field of area A = A x 30.50
Given : 30.50 A = 7350
            => A = 240.98 sq.metre

Therefore, $\frac{3}{2} a^{2} = 240.98$
                  =>  a = 12.67 metre
Hence, altitude length = 12.67 metre , and base length = 38.01 metre

Answer 2

Answer:

Step-by-step explanation:

We know the area of a triangle = x (base) x (altitude)

Let the altitude of the triangle = a

therefore, base length = 3a

=> area, A = x 3a x a

=> sq.metre

Price of levelling the field of area A = A x 30.50

Given : 30.50 A = 7350

            => A = 240.98 sq.metre

Therefore,

                  =>  a = 12.67 metre

Hence, altitude length = 12.67 metre , and base length = 38.01 metre.