Question

find the area of triangular plot whose sides in the ratio 3 ratio 5 ratio 7 and its perimeter is 300 m​

Answer 1

perimeter=sum of all sides

300=3x + 5x + 7x

300=15x

300/15=x

20=x

3x=3 x 20 = 60 m

5x=5 x 20= 100m

7x=7 x 20= 140m

area=1/2 x base x height

= 1/2 x 140 x 100

= 7000m²

Answer 2

Answered

THE SIDES OF A TRIANGULAR PLOT ARE IN THE RATIO 3:5:7 AND PERIMETER IS 300M. FIND ITS AREA BY HERONS FORMULA

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