Question

sides are 3:5:7 perimeter is 300 find area herons formula ​

Answer 1

Let the sides be 3x , 5x and 7x .

so which implies that

3x + 5x + 7x = 300

15x = 300

x = 300/15

x = 20 .

now the sides are 3x = 3*20 = 60 m

5x = 5*20 = 100 m

7x = 7*20 = 140 m

semi perimeter = 60 + 100 + 140 / 2

= 150 m

using herons' formula ;

area = root s (s-a) (s-b) (s-c)

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

= 150*90*50*10

= 1500 root 3 ( by prime factorisation )

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

Step-by-step explanation:

let 3:5:7=3x,5x&7x

3x+5x+7x=15x=300

x=300/15=20

perimeter=300

s=150

herons formula =√s(s-a)(s-b)(s-c)

=√150(150-3x)(150-5x)(150-7x)

=√150(150-3*20)(150-5*20)(150-7*20)

=√150(90)(50)(10)

=√6750000

=√6750000

=2598approx