Name: Areas Related to a Circle
Uploaded: 2019-07-19
Duration: 18 min 34 s
Description: Have you ever wondered why the area of the circle is πr^2? Let's learn more about the formula related to the area, circumferences, arc, and sector of a circle.

Question

The altitude of a field in the form of a triangle is half of its base. If the cost of irrigating the field at the rate of $₹ 280$ per hectare is $₹ 4480$ , find its base and altitude.

What is the importance of irrigation in agriculture?

Accepted Answer

Given: Rate $= ₹ 280$ per hectare, Cost $= ₹ 4480$

Therefore, Area in hectare $= \frac{cost}{Rate} = \frac{4480}{280} = 16$

Area in $m^{2} = 16 \times 10000 m^{2} = 160000 m^{2}$

Let Length of altitude $= x$ , Base $= 2 x$

Area of triangle $= \frac{1}{2} \times b \times h = 160000 m^{2}$

$\Rightarrow \frac{1}{2} \times (2 x) \times (x) = 179200$

$\Rightarrow x^{2} = 160000$

$\Rightarrow x = \sqrt{160000}$

$\Rightarrow x = 400 m$

Therefore, Base $= 2 x = 2 \times 400 = 800 m$

Altitude $= x = 400 m$

Irrigation helps to grow agricultural crops, maintain landscapes, and revegetate disturbed soils in dry areas and during periods of less than average rainfall. Irrigation also has other uses in crop production, including frost protection, suppressing weed growth in grain fields and preventing soil consolidation.

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