Prema had a triangulas feild with sides 240cm,200cm,360cm,where grew ragi.In another triangulas feild with two sides 240cm,320cm,adjacent to the previous feild,she wanted to grow carrot and beans as shown in fig . She divided the feild in 2 parts by joining the mid point of the longest side to the opposite vertex and grew carrots in one part and beans in the other part . How much area (in hartares) has been used for Ragi,Carrots and Beans
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Given Prema had a triangular field with sides 240 cm,200 cm,360 cm, where he grew ragi. In another triangular field with two sides 240 cm,320 cm,400 m adjacent to the previous field. She wanted to grow carrot and beans as shown in fig . She divided the field in 2 parts by joining the mid-point of the longest side to the opposite vertex and grew carrots in one part and beans in the other part . How much area (in hectares) has been used for Ragi, Carrots and Beans
- Given length of triangular field for ragi = 240 m,200 m and 360 m
- Length of triangular field for carrot and beans = 240 m,320 m, 400 m
- We need to find area of the field used for ragi, carrot and beans.
- Using heron,s formula to find area of triangle we get
- Area = √s(s – a)(s -b)(s – c)
- Now a = 200 m, b = 240 m, c = 360 m
- S = a + b + c / 2
- = 200 + 240 + 360 / 2
- = 800 / 2
- = 400 m
- Now area of triangle ABC = √400(400 – 200)(400 – 240)(400 – 360) m^2
- = √400 x 200 x 160 x 40 m^2
- = √512000000
- = 22,627.41 m^2
- We know that
- 10,000 m^2 = 1 hectare
- Therefore 22,627.41 hectare = 22,627.41 / 10,000
- = 2.262 hectares is the area for growing ragi.
- Again let a = 240 m, b = 320 m and c = 400 m
- S = a + b + c / 2
- = 240 + 320 + 400 / 2 m
- = 960 / 2 m
- = 480 m
- Now area of triangle will be = √s(s- a) (s – b) (s -c) m^2
- = √480 (480 – 240) (480 – 320) (480 – 400) m^2
- = √480 x 240 x 160 x 80
- = √48 x 24 x 16 x 8 x 10^4
- = √12 x 4 x 12 x 2 x 16 x 8 x 10^4
- = 12 x 2 x 16 x 10^2 m^2
- = 38,400 m^2
- So 10,000 m^2 = 1 hectare
- 38,400 m^2 = 38,400 / 10,000
- = 3.84 hectares.
- Area for growing ragi will be 1/2 the area
- = 1/2 x 3.84 hectares
= 1.92 hectares.
Therefore area for growing carrot and beans will be 1.92 hectares.
Reference link will be
https://brainly.in/question/4318903
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