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triangularfielda0with sides 240 m, 2another triangular field with sides 240 m, 320as a200 m, 360 m, where shelewheat. In another trianious field, she tm, 400 mted to grow potatoes and onions (see Fig. 12m adjacent to the2.11). She dividedopposite vertexs by joining the mid-point of the longest side to thedprew patafsed for wheatart and onions in the other part. How much area in hectarses, potatoes and onions? (d hectare 10000 m2) |
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Answer» 1)apply the Pythagorean theorem to verify if there is any rectangular triangletriangle ABC360²=200²+240²-------------> 19600=40000+57600--> is not rectangular triangletriangle BCD400²=320²+240²----> 160000=102400+57600----> 160000=160000----- > okthe triangle BCD is a rectangular trianglethe area of triangle BCD=(1/2)*320*240=38400 m²Area for potatoes--------------- > 38400/2=19200m²and Area for onions=Area forpotatoes=19200m² 2) by theformula of Heronfinds the area of atriangleof which all its sides are knowntriangleABCs-----------> semiperimeter=[360+200+240]/2=400 mA=[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 m²Area for wheat-------- > 22627.42 m² the total area isArea forpotatoes=19200m²Area foronions=19200m²Area for wheat=22627.42 m² total area=19200+19200+22627.42=61027.42 m² in hectares1 hectares---------------------- >10000 m² X------------------------------- > 61027.42 m² X=61027.42 /10000=6.10 hectares total area------> 6.10 HaArea forpotatoes=1.92 HaArea foronions=1.92 HaArea for wheat=2.26 Ha |
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