Question

the sides of a triangular plot are in the ratio 5:7:3 and its perimeter is 300m ?find its area​

Answer 1

Step-by-step explanation:

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

Answer:

Let the ratio of sides of ∆ be 5x : 7x : 3x

Perimeter = 300m

5x + 7x + 3x = 300

15x = 300

x = 300/15 = 20

Now,

1st side of ∆ = 5x = 5×20 = 100 m

2nd side of ∆ = 7x = 7×20 = 140 m

3rd side of ∆ = 3x = 3×20 = 60 m

s = (100 + 140 + 60)/2

= 300/2 = 150

Area of ∆ = √s(s-a)(s-b)(s-c)

= √150(150 - 100)(150 - 140)(150 -60)

= √150 × 50 × 10 × 90

= √( 30 × 5 × 5 × 10 × 30 × 3)

= 30 × 5 × 10 × √3

= 1500 √3 sq. m

Hence , the area of ∆ is 1500 √3 sq. m .

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