Question

the base of a triangular garden is three times its altitude . if the cost of grassing the garden at rs 685 per hectare is rs 9247.50 , find its base and altitude.
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Answer 1

Answer: base= 900 m , altitude= 300 m

Step-by-step explanation:

Alright lets begin with knowing what hectare is !

Hectare is a unit for area.

1 hectare=10000 sq meter

now, let's jump right into the question !

rate of grassing the garden = rs 685 per hectare

total cost of grassing = rs 9247.50

∴ area of the garden= total cost of grassing / rate of grassing

                                  = 9247.50/685 = 13.5 hectare

area in sq meter= 13.5 x 10000 = 135000 sqm

now lets try to visualize what's going on with this triangular field !

according to the question , the base is three times its altitude (height).

let's assume that the length of the altitude is h meters.

so the length of base will be = 3h meters.

(okay, if you cant visualize the figure refer to the image attached below.)

now, we know that area of a triangle= 1/2 x base x altitude

∴ 1/2 x h x 3h = 135000

⇒h² = 135000x2/3

⇒h² = 90000

⇒h=√ 90000

⇒h=300 meters

now, base= 3 x h = 3x 300 = 900 meters

i hope u find this helpful :)

Answer 2

if the cost of grassing the garden at rs 685 per hectare is rs 9247.50 , find its base and altitude.