Question

A farmer has a triangular field with sides 200m, 300m and 400m in which he grew wheat and in another triangular field with sides 200m, 320m and 360m , he grew vegetables. calculate the area of the land in which wheat and vegetables are produced ? how can you motivate the students and make them aware about the uses of both the food products mentioned above?

Answer 1

one farm by using scalene triangle area formula I think wheat filed is more

Answer 2

Answer:

Total area of land used = 60886.98 meter²

Step-by-step explanation:

Sides of triangular field in which Wheat is grown :

a = 200 m , b = 300 m , c = 400 m

$s = \frac{a+b+c}{2}\\\\\implies s = \frac{900}{2}=450\thinspace m$

$\text{Area of the field of wheat = }\sqrt{s(s-a)(s-b)(s-c)}\\\\\implies Area=\sqrt{450\cdot (450-200)\cdot (450-300)\cdot (450-400)}\\\\\implies Area = \sqrt{450\times 250\times 150\times 50}\\\\\implies Area = \sqrt{843750000}=29047.38\text{ meter}^2$

Sides of triangular field in which vegetables are grown :

a = 200 m , b = 320 m , c = 360 m

$s = \frac{a+b+c}{2}\\\\\implies s = \frac{880}{2}=440\thinspace m$

$\text{Area of the field of vegetable = }\sqrt{s(s-a)(s-b)(s-c)}\\\\\implies Area=\sqrt{440\cdot (440-200)\cdot (440-320)\cdot (440-360)}\\\\\implies Area = \sqrt{440\times 240\times 120\times 80}\\\\\implies Area = \sqrt{1013760000}=31839.60\text{ meter}^2$

Total area of land used = 29047.38 + 31839.60

                                        = 60886.98 meter²