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Sum

The altitude and the base of a triangular field are in the ratio 6: 5. If its cost is ₹ 49,57,200 at the rate of ₹ 36,720 per hectare and 1 hectare = 10,000 sq. m, find (in metre) dimensions of the field.

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#### Solution

Total cost = ₹ 49,57,200

Rate = ₹ 36,720 per hectare

The total area of the triangular field

= `4957200/36720 xx 10000 "m"^2 = 1350000 "m"^2`

The ratio in altitude and base of the field = 6: 5

Let altitude = 6x

and base = 5x

∴ Area = `1/2 "Base" xx "Altitude"`

⇒ 1350000 = `1/2 xx 5x xx 6x`

⇒ `15x^2 = 1350000 ⇒ x^2 = 1350000/15`

⇒ `x^2 = 90000 = (300)^2`

∴ x = 300

∴ Base = 5x = `5 xx 300 = 1500` m

and altitude = `6x = 6 xx 300 = 1800`m

Concept: Perimeter of Triangles

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