Question

The sides of a triangular plot are in the ratio 3:5:7 and its perimeter is 300m. Find its ratio.

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Answer 1

$\huge\star\underline\mathfrak\red{Answer:-}$

Suppose that the sides in metres are 3x , 5x and 7x.

Then, we know that 3x+5x+7x = 300 (perimeter of the ∆)

therefore, 15x = 300 , which gives x= 20 .

So, the sides of the ∆ are 3 × 20m, 5×20m and 7×20m.

i.e., 60m , 100m and 140m.

We have s = 60+100+140m/2 = 150m

Area will be = √150(150-60) (150-100) (150-140)

= √150×90×50×10m^2

= 1500√3m^2

Answer 2

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