The sides of a triangular field are 41m, 40m, 900 cm. Each rose bed requires 180 sq. cm of are. How many rose beds can be prepared in the field?

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Solution

We have 900 cm = 9 m
By Heron's formula.
Area of a triangular= √s×(s-a)(s-b)(s-c) ,where a,b,c are sides of the triangle and s is the semi perimeter.
s=(a+b+c)/2=(41+40+9)/2=45
so, area of the field=√[45×(45-41)(45-40)(45-9)] = √(45 × 4 × 5 × 36) = √32400 = 180m^2 =1800000cm^2.
now, space needed for a rose bed = 180cm^2.
so, number of rose beds = 1800000/180 = 10000.

So there can be 10000 rose beds prepared

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