# 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) - Mathematics

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.

#### 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 = 1800m

Concept: Perimeter of Triangles
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#### APPEARS IN

Selina Concise Mathematics Class 8 ICSE
Chapter 20 Area of a Trapezium and a Polygon
Exercise 20 (A) | Q 12 | Page 224