Question

The Base of the triangular field is three times its altitude. If the cost of cultivating the field @ 24.60 per hectare is Rs 332.10,find its Base and height​

Answer 1

★Given:-

• The Base of the triangular field is three times its altitude.
• The cost of cultivating the field at 24.60 per hectare is Rs 332.10

★To find:-

• Its base and height.

★Solution:-

Let the height of triangular field is 'h'.

Given that base of the triangular field is three times its altitude.

Therefore,

• Base = 3h

Using the formula,

✦Area = 1/2×base×height

Putting values,

Area of triangular field:-

➜(1/2)×base×height

➜(1/2)×3h×h

➜3h²/2

Given,

• Cost of cultivating 1 hectare = Rs.24.60
• Then Total cost of cultivating whole field = Rs.332.10

Area of field = Total cost/Rate

                      = 332.10/24.60

                     = 13.5hectare

We know,

1 hectare = 10000 m

∴13.5 hectare = 135000 m

Therefore,

➜3h²/2 = 135000

➜h² = 135000 × (2/3)

➜h = √90000

➜h = 300

We have,

• Height = x
• Base = 3x

Therefore,

➜Height =300 m

➜Base = 3x

        =3(300)

         =900 m

Hence,its base and height are 900m & 300m respectively.

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