Question

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

Answer 1

Given -

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

To find -

• Base and height of triangular field

Solution -

• Let the height be x and its base be 3x

If the cost of cultivating the field at Rs.36 per hectare is Rs.486.

• Area of triangular field

→ Total cost/Rate

→ 486/36

→ 13.5 hectare

Focus Zone : 1 hectare = 10000m²

• Area of triangular field = 13.5 × 10000 = 135000 m²

According to the question

→ Area of triangular field = 135000

→ ½ × base × height = 135000

→ ½ × 3x × x = 135000

→ 3x²/2 = 135000

→ 3x² = 270000

→ x² = 270000/3

→ x² = 90000

→ x = √90000

→ x = ± 300 m

Focus Zone : Length never be in negative

•°• Height of triangular field = x = 300m

•°• Base of triangular field = 3x = 900m

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Answer 2

$\underline{\boxed{\bold\red{Question}}}$

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

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$\underline{\boxed{\bold\blue{Answer}}}$

$\orange{Cost \: of \: the \: cultivated \: field }\blue{= 486}$

$\orange{Rate}\blue{ = 36Rs}$

$\orange{Area \: of field }\blue{= \dfrac{486}{36}}$

$\blue{13.5 \: hectare}$

$\green{1 \: hectare = 10000m²}$

$\orange{Area \: of \: field}\blue{ = 13.5×10000}$

$\blue{135000m²}$

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$\orange{Area \: of \: triangle} \green{= \dfrac{1}{2}×base×height}$

$\green{base = 3×height}$

$\green{\dfrac{1}{2}×3×height×height= \: 135000m²}$

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$\green{height² = 135000×\dfrac{2}{3}=90000m²}$

$\orange{height}\blue{ = 300m}$

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$\green{base = 3×height}$

$\blue{=3×300}$

$\blue{=900m}$

Hence, Height = 300m base = 900m

[Hope this helps you.../]