Question

The sides of a triangular field are 41m, 40m and 9m. Find the number of flower beds that can be prepared in the field, if each flower bed needs 900cm2 space.

Answer 1

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.
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 flower bed = 900cm^2.
so, number of flower beds = 1800000/900 = 2000.

Answer 2

Side a = 41m

Side b = 40m

Side c = 9m

Perimeter = 41+40+9

= 90m

Semi-perimeter = perimeter/2

= 90/2

= 45m

S - a = 45-41 = 4m

S - b = 45-40 = 5m

S - c = 45-9=36m

According to heron's formula area = ✓s(s-a)(s-b)(s-c)

=✓45*4*5*36

=✓2*2*2*2*3*3*3*3*5*5

=2*2*3*3*5

=4*9*5

=36*5

=180m

Space needed for each flower bed = 900cm

Total area in cms = 180*100

=18000

So,number of flower beds to be allocated = 18000/900

=20 flower beds

Hope this helps

Regards

Rohan Dheeraj :)