Question

find the ratio of a triangle whose sides are in the ratio 5:4:3 and it's perimeter is the 48m also find the cost of ploughing it at the ratio of rupees 3 per m²​

Answer 1

Answer:

sides are 20 m, 16 m and 12 m and cost of ploughing is Rs.18

Step-by-step explanation:

perimeter of triangle= 5x + 4x + 3x

48=12x

x=4

hence sides are : 5x4=20m

4x4=16m

3x4=12m

cost of ploughing= area of triangle x rate of ploughing per sq.m

= 6x3

=Rs.18

Answer 2

Given, Side of triangle are in ratio 3:4:5 and their perimeter 144 cm

Let the sides of triangle be 3x,4x,5x

Perimeter 3x+4x+5x= 144 cm

12x=144

∴x=12

Then sides of triangle are 3x= 3×12= 36 cm,

                                           4x= 4×12= 48 cm,

                                           5x= 5×12= 60 cm.

Now,Semi perimeter, s=  

2

Sumofsidesoftriangle

​  

 

                                       

=  

2

36+48+60

​  

=72cm

Using heron's formula, Area of triangle=  

s(s−a)(s−b)(s−c)

​  

 

                                                               

=  

72(72−36)(72−48)(72−60)

​  

 

                                                               

=  

72×36×24×12

​  

=864cm  

2

 

Using altitude, area of triangle=  

2

1

​  

× base × altitude =864cm  

2

 

                                                 =  

2

1

​  

×60× altitude =864

∴ altitude =  

60

864×2

​  

=28.8cm

So, altitude corresponding to largest side is 28.8 cm