Question

Find the area of the triangular garden whose sides are 40m,90m and 70m [use root 5=2.24]

Answer 1

Solution - 

Area of a triangle whose three sides are given is given by Heron's formula.

A = sqrt (s (s - a) ( s - b) (s - c)) 

Where s is the half perimeter.

s = (a + b + c) / 2 

Given: a = 40m, b = 90m, c = 70m

s = (40 + 90 + 70) / 2
   
   = 200/2
  
   = 100 m

Area of the triangle A = sqrt (s (s - a) ( s - b) (s - c))
              
                                      = sqrt (100 * (100 - 40) * (100 - 90) * ( 100 - 70))
  
                                      = sqrt ( 100 * 60 * 10 * 30)
 
                                      = 10 sqrt (18000)
   
                                       = 10 sqrt (3600 * 5)
    
                                       = 10 * 60 * sqrt 5
        
                                       = 10 * 60 * 2.24
                            
                                       = 1344 sq. m

Area of the triangular garden = 1344 sq. m

Answer 2

Solution:-
Let a = 40 m, b= 90 m and c = 70 m
s = (a+b+c)/2
⇒ (40+90+70)/2
⇒ 200/2
s = 100
By Heron's formula of area of triangle
= √s(s-a)(s-b)(s-c)
⇒ √100(100-40)(100-90)(100-70)
⇒ √100*60*10*30
⇒ 10√18000
⇒ 10×60√5
= 10×134.4
= 1344 m²
Answer.