Question

The base of triangular field is three times its height if the cost of cultivating the field is ₹36 per hectare is 486 , find its base and height

Answer 1

The base of triangular field is three times of its height. and cost of cultivating the field is 36 Rs. per hectare is 486.

To find : The base and height of triangular field.

solution : area of triangular field = total cost of cultivating the field/rate

here cost of cultivating the field = 486 Rs.

rate = 36 Rs/hectare

so, area of field = 486/36 = 13.5 hectare

we know, 1 hectare = 10000 m²

so, area of field = 13.5 × 10000 = 135000 m²

a/c to question,

base = 3 × height .......(1)

but area of triangle = 1/2 × base × height

so, area of field = 135000 m²

⇒1/2 × base × height = 135000 m²

⇒1/2 × 3 × height × height = 135000 m² [ from eq (1).]

⇒height² = 135000 × 2/3 = 90000 m²

⇒height = 300 m

base = 3 × height = 3 × 300 = 900 m

Therefore base = 900 m and height = 300 m

Answer 2

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