Question

Find area of a triangle whose sides are in the ratio 3:4:5 and altitude on the largest side is 28.8 cm.

Answer 1

Well here we know the ratio of all sides of triangle i.e. 3:4:5
Let the common multiple be "x"

There fore the sides are 3xcm,4xcm,5xcm
and here we will use herons formula
For that we need semiperimeter =a+b+c/2=3x+4x+5x/2=12x/2=6x

and by herons formula we get
Area=[s(s-a)(s-b)(s-c)]^1/2
Area=[6x(6x-3x)(6x-4x)(6x-5x)]^1/2
Area=[6x*3x*2x*x]^1/2
Area=[36x^4]^1/2
Area=6x^2 cm^2____________(1)

we know that the
here the height is drawn on the longest side i.e. 5x
therefore here 5x is the longest side
we know area of triangle (A)=1/2*base *height
therefore height=2*area/base
28.8=2*(6x^2/5x)
28.8= 2(1.2x)
28.8=2.4x
x=28.8/2.4=12
therefore value x =12

hence the area of triangle is =6x^2=6*144=864cm^2

Hope this helped u :-)

Answer 2

The sides of the triangle are 3:4:5
so let them be 3x ,4x 5x
Altitude on the largest side is 28.8cm 
so here base= 5x
             Height= 28.8 cm
Using the heron's Formula
 semi-perimeter= 3x+4x+5x/2
                         =12x/2
                         = 6x
area of triangle= √s(s-a)(s-b)(s-c)
                        = √6x(6x-3x)(6x-4x)(6x-5x)
                        = √6x*3x*2x*x
                        =√2*3*x*3*x*2*x*x
                        =2*3*x*x
                        =6x²
As we know, area of triangle= 1/2*b*h
                                       6x²  =  1/2*5x*28.8
                                        x² = 5x*14.4/6
                                        x² = 72x/6
                                        x² = 12x
                                       x*x/x=12
                                         x=12
  so, 6x² = 6*(12)²
              =864cm²