The base of a triangular field is 3 times it’s height. If the cost of cultivating the field is ₹36.72 per hectare is ₹495.72. Find its base and height
Answers
Step-by-step explanation:
Given :-
The base of a triangular field is 3 times it’s height.
The cost of cultivating the field is ₹36.72 per hectare is ₹495.72.
To find :-
Base and height of the field
Solution :-
Let the height of the triangular field be h m
Then, the base of the triangular field
= 3 times its height
= 3×h m
Therefore, Base = 3h m
We know that
Area of a triangle = ½ bh sq.units
Where, b = base and h = height
Area of the given triangular field
=> A = ½×3h×h m²
=> A = 3/2 h² m²
Area of the triangular field = 3/2 h² m² -----(1)
Given that
The cost of cultivating the field per 1 hectare
= Rs. 36.72
Total cost of cultivating the triangular field
= Rs. 495.72
Area of the triangular field
= Total Cost / Cost per 1 hectare
= 495.72 / 36.72
= 13.5 hectare
Area of the field = 13.5 hectare
We know that
1 hectare = 10000 m²
=> 13.5 hectare = 13.5×10000 m²
=> 13.5 hectare = 135000 m²
Area of the triangular field = 135000 m² ----(1)
From (1) & (2)
=> 3/2 h² = 135000
=> h² = 135000×2/3
=> h² = 270000/3
=> h² = 90000
=> h = ±√90000
=> h = ±300 m
Therefore, h = 300 m
Since, Height can't be negative.
Therefore, Height of the triangular field = 300 m
If h = 300 m then 3h = 3(300) = 900 m
Therefore, The base of the field = 900 m
Answer :-
The base of the triangular field = 900 m
The height of the triangular field = 300 m
Check :-
The base of the triangular field = 900 m
The height of the triangular field = 300 m
base = 900 m = 3×300 m
Base = 3 times its height
Area of the triangular field
=> A = ½×900×300 m²
=> A = 270000/2 m²
=> A = 135000 m²
=> A = 135000/10000 hectare
=> A = 13.5 hectare
The cost of cultivating the field per 1 hectare
= Rs. 36.72
Total cost of cultivating field of 13.5 hectare
= 13.5×36.72
= Rs. 495.72
Verified the given relations in the given problem.
Used formulae:-
→ Area of a triangle = ½bh sq.units
- Where, b = base
- Where, b = base h = height
→ 1 hectare = 10000 m²
Given :
The base of a triangular field is 3 times it’s height.
and, The cost of cultivating the field is ₹36.72 per hectare is ₹495.72.
To Find :
Base and Height
Solution :
A.T.Q,
Base of ∆ field = 3 x h
= 3h m
and, by using Area of ∆ = ½ × b × h
⇒ ½ x 3h x h
⇒ 3h²/2 m² ---------- eq(1)
The cost of cultivating the field is ₹36.72 per hectare is ₹495.72.
➻ Area of Field = 495.72/36.72
= 13.5 hectares
we know that, 1 hectare = 10,000 m²
Area of Triangular Field = 13.5 x 10,000
= 1,35,000 m² ------- eq(2)
from eq(1) , eq(2)
⇒ 3/2 • h² = 135000
⇒ h² = 135000 • ⅔
⇒ h = √90000
⇒ h = ± 300 m
⇒ h = 300m [since, height can't be in negative]
then,
⇒ Base = 3 • 300
⇒ Base = 900m
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FINAL ANSWER :
Base of Field = 900m
Height of Field = 300m