The base of a triangular field is three times its altitude. If the cos

1.	The base of a triangular field is three times its altitude. If the cost of sowing the field at ₹ 58 per hectare is ₹ 783, find its base and height.
Answer» Take x and the height and 3x as the base of the triangular field 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 = ₹ 58 Total rate of sowing the field = ₹ 783 So we can find the total cost by Total cost = Area of the field × ₹ 58 By substituting the values (3/2) x² × (58/10000) = 783 By cross multiplication x² = (783/58) × (2/3) × 10000 On further calculation x² = 90000 By taking the square root x = √90000 So we get x = 300 m Base = 3 × 300 = 900 m Therefore, base = 900 m and height = 300 m.

The base of a triangular field is three times its altitude. If the cost of sowing the field at ₹ 58 per hectare is ₹ 783, find its base and height.

Answer»

Take x and the height and 3x as the base of the triangular field

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 = ₹ 58

Total rate of sowing the field = ₹ 783

So we can find the total cost by

Total cost = Area of the field × ₹ 58

By substituting the values

(3/2) x² × (58/10000) = 783

By cross multiplication

x² = (783/58) × (2/3) × 10000

On further calculation

x² = 90000

By taking the square root

x = √90000

So we get

x = 300 m

Base = 3 × 300 = 900 m

Therefore, base = 900 m and height = 300 m.