Question

The perimeter of a triangular field is 300 cm and its sides are in the ratio 3:5:2. Find its area.
Please provide step by step answer.

Answer 1

Answer :

• 0
• Thus, A triangle with 0 area is formed which means points are collinear.

Given :

• The perimeter of a triangular field is 300cm
• Sides are in the ratio is 3 : 5 : 2

To find :

• Area

Solution :

• Let the ratio be 3x , 5x and 2x
• Perimeter of triangular field is 300cm

According to question,

》3x + 5x + 2x = 300

》10x = 300

》x = 300/10

》x = 30cm

So, Sides are,

• 3x = 3(30) = 90cm
• 5x = 5(30) = 150cm
• 2x = 2(30) = 60cm

Sides are 90cm , 150cm , 60cm.

As we know that,

• s = a + b + c / 2

》s = 90 + 150 + 60 / 2

》s = 300/2

》s = 150cm

Now we have to find the area of triangular field

We know that, Area of triangular field :  heron's formula :

• √s(s - a) (s - b) (s - c)

Where, a is 90 , b is 150 , c is 60 and s is 150

》√s(s - a) (s - b) (s - c)

》√150(150 - 90) (150 - 150) (150 - 60)

》√150 × 60 × 0 × 90

》√0

》0

Hence , Area of triangular field is 0cm²

Thus, A triangle with 0 area is formed which means points are collinear.

Answer 2

Step-by-step explanation:

Given : The Side Of a Triangular Plot are in the ratio 3:5:7 and Perimeter is 300 cm

Find : Area Of A Triangular Plot

Solutions : Let the Side Of a triangular field is 3x , 5x and 7x

3 x + 5 x + 7 x = 300 ( The Perimeter of Triangular field)

15 x = 300

x = 300/15 ( Divided by both)

x = 20

Then the side of a triangular Plot is

Now Putting Value X in Equation

3 x = 3×20 = 60

5 x = 5 × 20 = 100

7 x = 7 × 20 = 140

Now Applying Herons Formula

To Find Area

Area = √ s ( s - a) ( s - b) ( s - c)

Now Putting Value In Formula

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

Area = 1500 √ 3 m^2

The Area Of A Triangular Plot Is 1500√3m^2