Question

the parameter of rectangular field is 270 metre and its sides are in the ratio 25 : 17 : 12 find its area ​

Answer 1

Corrected Question :

The perimeter of triangular field is 270 metre

and it's sides are in the ratio 25 : 17 : 12. Find its

area .

Answer:

The area of the triangular field : 2,250 m² ( approx )

Given:

➨ The perimeter of triangular field is 270 metre .

➨ It's sides are in the ratio 25 : 17 : 12.

To Find :

The area of the triangular field.

Solution:

(Refer the attachment)

We are given,

The sides of the triangular field are in the ratio

➺ 25 : 17 : 12.

Let the sides of the triangular field be 25m , 17m , and 12m.

We are also given ,

➨ The perimeter of triangular field is 270 metre .

⛬ 25m + 17m + 12m = 270.

➪ 54m = 270 .

➪ m = 270 / 54

➪ m = 5

Hence , The three sides of the triangular field are.

25m = 25 × 5 = 125 metre.

17m = 17 × 5 = 85 meter.

12m = 12 × 5 = 60 metre.

We know ,

$semi \: Perimeter \: \: = \frac{perimeter}{2}$

$semi \: perimeter \: = \: \frac{270}{2}$

$semi \: perimeter \: = 135$

We know,

$area \: of \: triangle = \sqrt{s(s - a)(s - b)(s - c)}$

$area \: of \: triangle \: = \sqrt{135 \times (135 \times (135 - 125) \times (135 - 85) \times (135 - 60)}$

$area \: of \: triangle \: = \sqrt{135 \times 10 \times 50 \times 75}$

$area \: of \: triangle \: = \sqrt{5,062,500}$

Area of triangular field = 2,250( approx ) m²

Answer 2

Correct Question :

The perimeter of triangular field is 270 metre and its sides are in the ratio 25 : 17 : 12. find its area .

Solution :

Given :

• Perimeter of the triangular field = 270 metre.

• Its sides are in the ratio 25 : 17 : 12.

To find :

• Area of triangular field =?

Step-by-step explanation :

It is Given that,

The sides of the triangular field are in the ratio 25 : 17 : 12.

Now,

Let the sides of the triangular field be 25x , 17x , and 12x.

It is Given that ,

The parameter of triangular field is 270 metre .

We know that,

Perimeter = Sum of all sides.

Substituting the values, we get,

➮ 270 = 25x + 17x + 12x

➮ 270 = 54x

Or, 54x = 270

➮ x = 270 / 54

➮ x = 5

Therefore, We got the value of, x = 5.

Hence ,

The three sides of the triangular field,

25x = 25 × 5 = 125 metre.

17x = 17 × 5 = 85 meter.

12x = 12 × 5 = 60 metre.

Now

Area of traingle, (By heron's formula)

S = 125+ 85 + 60/2

= 270/2

= 135

Heron's formula = √(s(s-a)(s-b)(s-c)

Substituting the values in the above formula, we get,

=√(135×(135 - 125)(135 - 85)(135 - 60)

=√(135 × 10 × 50 × 75)

=√5,062,500

= 2250

Therefore, Area of the triangular plot = 2250 m².