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 square meter, find (in meter) dimensions of the field.

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Solution

Let the altitude of field be h and base be b

Thus h:b = 6:5
h= 6/5 b
area of field = 1/2 bh
in hectares, area of field = (1/10000)1/2bh

According to question
Cost of 1 hectare = 36,720 rupees

and
total cost is 49,57,200 rupees
Thus,

Total cost =
cost of 1 hectare total area
49,57,200
= 36.720 * (1/20000) bh

putting h = 6/5b

49,57,200 =
36,720 * (1/20000) 6/5b^2
b^2 = 123.456
b= 11.11 m
thus h= 6/5 * 11.11
h = 1.2*11.11
h = 13.332 m

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

Area of the given triangular field $= \frac{C o s t o f t h e f i e l d}{R a t e} = \frac{49, 57, 200}{36, 720}$ hectare

=135 hectare

$= 135 \times 10, 000$ sq. m=1350000 $m^{2} .$

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