the base of a triangular field is three times its altitude.If the cost of watering the field at 96 rupees per hectare is rupees 3600, find the measure of the base and height.
Answers
Answer:
Let ,
the altitude of the triangle be y
Then the base will be 3y
Area of triangle is 1/2 x base x altitude
=1/2 x 3y xy
= 1/2 x
= 3y/2
Cost of sowing the field at rs 58 per hectare
= 58 × 3x2/2 = 87x2
Therefore, 87x2 = 783
= 783/87 = 9
⇒ y = 3
Base = 3(3) = 9
Hence base is 9 and altitude is 3.
Step-by-step explanation:
We know that
Area of triangle = ½ × b × h
By substituting the values
Area of triangle = ½ × x × 3x
So we get Area of triangle = 3/2 x2
1 hectare = 1000 sq. metre
It is given that Cost of sowing the field per hectare = ₹ 96
Total rate of sowing the field = ₹ 3600
So we can find the total cost by
Total cost = Area of the field × ₹ 96
By substituting the values (3/2) x2 × (96/10000) = 3600
By cross multiplication x2 = (3600/96) × (2/3) × 10000
On further calculation
x2 = 250000
By taking the square root x = √250000
So we get x = 500 m Base = 3 × 500 = 1500 m Therefore, base = 1500 m and height = 500 m