Question

The base of a triangular field is three times it's altitude. If the cost of sowing the field at Rs 960 is Rs 12960 them find the base and also the Height of triangle.​

Answer 1

✬ Base = 900 m ✬

✬ Altitude = 300 m ✬

Step-by-step explanation:

Given:

• Base of a triangular field is 3 times the altitude.
• Cost of sowing field at Rs 960 is Rs 12960.

To Find:

• What is the meaure of base and height ?

Solution: Let the altitude of field be x. Therefore,

➟ Base of field = 3(x)

Here, Total cost of sowing field is Rs 12960 and rate per hectare is Rs 960.

∴ Area = Total cost/Rate

➼ (12960/960) hectares

➼ 13.5 hectares

• 1 hectare = 10000 m² so
• 13.5 hectares = 13.5(10000)m²

➼ Total area of field = 135000 m²

As we know that

★ Area of ∆ = 1/2(Base)(Height) ★

$\implies{\rm }$ 135000 = 1/2(3x)(x)

$\implies{\rm }$ 135000 = 3x²/2

$\implies{\rm }$ 135000(2) = 3x²

$\implies{\rm }$ 270000/3 = x²

$\implies{\rm }$ 90000 = x²

$\implies{\rm }$ √90000 = x

$\implies{\rm }$ 300 = x

So, Measure of

➭ Altitude is x = 300 m

➭ Base is 3x = 3(300) = 900 m

Answer 2

Answer:

Base = 900 m ✬

✬ Altitude = 300 m ✬

Step-by-step explanation:

Given:

Base of a triangular field is 3 times the altitude.

Cost of sowing field at Rs 960 is Rs 12960.

To Find:

What is the meaure of base and height ?

Solution: Let the altitude of field be x. Therefore,

➟ Base of field = 3(x)

Here, Total cost of sowing field is Rs 12960 and rate per hectare is Rs 960.

∴ Area = Total cost/Rate

➼ (12960/960) hectares

➼ 13.5 hectares

1 hectare = 10000 m² so

13.5 hectares = 13.5(10000)m²

➼ Total area of field = 135000 m²

As we know that

★ Area of ∆ = 1/2(Base)(Height) ★

\implies{\rm }⟹ 135000 = 1/2(3x)(x)

\implies{\rm }⟹ 135000 = 3x²/2

\implies{\rm }⟹ 135000(2) = 3x²

\implies{\rm }⟹ 270000/3 = x²

\implies{\rm }⟹ 90000 = x²

\implies{\rm }⟹ √90000 = x

\implies{\rm }⟹ 300 = x

So, Measure of

➭ Altitude is x = 300 m

➭ Base is 3x = 3(300) = 900 m