6. The base of a triangular field is three times its height. If the co

1.	6. The base of a triangular field is three times its height. If the cost of cultivating the fieldat 36 per hectare is + 486, find its base and height (1 hectare = 10000 m²).
Answer» ANSWER: Base = 900 m and height = 300 m Step-by-step explanation: 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

6. The base of a triangular field is three times its height. If the cost of cultivating the fieldat 36 per hectare is + 486, find its base and height (1 hectare = 10000 m²).

Answer»

Base = 900 m and height = 300 m

Step-by-step explanation:

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