Question

A triangular field is in the shape of an isosceles triangle. The altitude and the base

are in the ratio 6:5.If it costs Rs 5250 at the rate of Rs.350 per hectare to grow

some crops in it, find the dimensions of the fie​

Answer 1

Area of an Isosceles Triangle

The base of the field is 500m, while the altitude of the field is 600m

Step-by-step explanation:

Let the unit be x.

The altitude and base are in the ratio of 6:5, i.e., 6x and 5x, respectively.

The total cost needed for growing crops is Rs 5250, at the rate of Rs 350/ hectare.

Hence,

The area of this field is = Total cost / rate per hectare

                  = 5250/ 350 = 15 hectares

The area of the isosceles field is 15 hectares.

Thus;

Area of isosceles triangle = ½ x base x height

The base and height are 5 x and 6 x respectively

So;

½ 5x * 6x = 15

15 x2  = 15

Thus, x2 = 1 hectare

1 hectare =10000 sq m

Hence, x = 100 m

The base of the field is 5x = 500 m

Altitude of the field is 6x = 600 m