Mohan inherited a triangular field with sides 240m,200m, and 360m, where he grew wheat . In another triangular field with sides 240m,320m,and 400m adjacent to the previous field, he wanted to grow potatoes and onions.
he divided the field into 2 parts by joining the mid point f the longest side to the opposite vertex and grew potatoes in one part and onions in other part. how much area(in hectares) has been used for wheat, potatoes and onions?

Question

17-02-2018
Mathematics

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Mohan inherited a triangular field with sides 240m,200m, and 360m, where he grew wheat . In another triangular field with sides 240m,320m,and 400m adjacent to the previous field, he wanted to grow potatoes and onions.
he divided the field into 2 parts by joining the mid point f the longest side to the opposite vertex and grew potatoes in one part and onions in other part. how much area(in hectares) has been used for wheat, potatoes and onions?

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calculista calculista · Answer 1 · 2018-02-26T15:36:19+01:00

see the attached figure with letters

1) apply the Pythagorean theorem to verify if there is any rectangular triangle
triangle ABC
360²=200²+240²-------------> 19600=40000+57600--> is not rectangular triangle
triangle BCD
400²=320²+240²----> 160000=102400+57600----> 160000=160000----- > ok
the triangle BCD is a rectangular triangle
the area of triangle BCD=(1/2)*320*240=38400 m²
Area for potatoes--------------- > 38400/2=19200  m²
and Area for onions=Area for potatoes=19200  m²

2) by the formula of Heron finds the area of a triangle of which all its sides are known
triangle ABC
s-----------> semiperimeter=[360+200+240]/2=400 m
A=[s*(s-a)*(s-b)*(s-c)]^(1/2)-----> [400*(400-360)*(400-200)*(400-240)]^(1/2)
A= [400*(40)*(200)*(160)]^(1/2)=22627.42 m²
Area for wheat-------- > 22627.42 m²

the total area is
Area for potatoes=19200  m²
Area for onions=19200  m²
Area for wheat=22627.42 m²

total area=19200+19200+22627.42=61027.42 m²

in hectares
1 hectares---------------------- >10000 m²
X------------------------------- > 61027.42 m²

X=61027.42 /10000=6.10 hectares

total area------> 6.10 Ha
Area for potatoes=1.92 Ha
Area for onions=1.92 Ha
Area for wheat=2.26 Ha