Question

The sides of a triangular plot are in ratio of 3:5:7 and its perimeter is 900m. Find it’s area

Answer 1

Let the sides of the triangle be 3x, 5x and 7x repsectively and since the perimeter is 300m

So, 3x + 5x + 7x=300

15x=300

x=300/15

x=20 m

so,length of one side=60 m

length of second side=100 m

and length of third side=140 m

Now perimeter=300m

therefore semi-perimeter=150 metre

 

now according to herons formula -

Area = root 150* (150-60) * (150-100) * (150-140)

= root 150 * 90 * 50 * 10

= root 30*5 * 30*3 * 5*10 *10

= root 30^2 * 5^2 * 10^2 *3

= 30 * 5 * 10 * root 3

= 1500 root 3

Answer 2

let the sides be 3x, 5x and 7x respectively
perimeter =  900m
3x+5x+7x=900
15x=900
x=900/15
x=60
now the sides are
3x=3 * 15=45m
5x= 5* 15 = 75m
7x= 7* 15=105m
Now use the HERON'S Formula to calculate the area