Question

the side of a triangular field are 4m,5m,6m.find the number of rose beds that can prepared in the field,if each rose bed,on an average needs 800 cmsq space

Answer 1

given sides of triangular field are 4m , 5m ,6m

converting these sides in cm

sides are , 400 cm , 500 cm , 600 cm

by using Heron's formula ,
area of triangular field is ,

= √s(s-a)(s-b)(s-c)

where a, b , c are sides of triangular field and s is half of perimeter

s = a+b+c/2
= 400+500+600/2
= 1500/2
=750

therefore area = √750(750-400)(750-500)(750-600)

area = √750 × 350 × 250 × 150
= 10 ×10 √75×35×25×15
= 100 √ 15×5×7×5×5×5×15
= 100 ×5×5×15 √7
= 37500√7 sq cm
= 99215.67 sq cm

now a single rose bed needs 800 sq cm space

therefore , total rose beds = 99215.67/ 800

= 124 beds