Question

the side of a triangular park are in the ratio of 2:6:7 and it's perimeter is 300m . Then it's area is
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Answer 1

Given:-

• Ratio of side of triangle = 2:6:7

• Perimeter of triangle = 300 m

To Find:-

• Area of triangle .

Solution:-

As we know that Perimeter of triangle is the sum of the side of triangle.

Let , the ratio be 2x , 6x , 7x

2x + 6x +7x = 300

Or, 15x = 300

Or, x = 300/15

Or, x = 20m

Put the value of x we get

S1 = 2x = 2×20 = 40m

S2 = 6x = 6×20 = 120m

S3 = 7x = 7×20 = 140m

Semiperimeter of triangle = S1+S2 +S3/2

= 40+120+140/2

= 300/2 = 150

S = 150m

Now , calculating the area of triangle. By using Heron's Formula

$area \: of \: triangle \: = \sqrt{s(s - s1)(s - s2)(s - s3)} \\ \\ = \sqrt{150(150 - 40)(150 - 120)(150 - 140)} \\ \\ = \sqrt{150 \times 110 \times 30 \times 10} \\ \\ = \sqrt{4950000} \\ \\ = 2224.85 {m}^{2}$

Therefore the area of triangle is 2224.85 m².

Answer 2

Given :

The ratio of the sides of a triangular park = 2 : 6 : 7.

The perimeter of a triangular park = 300 m

To Find :

The area of a triangular park.

Solution :

First, we need to find the sides of a triangular park.

Let,

The first side be 2x.

The second side be 6x.

The third side be 7x.

Given,

Perimeter of the park = 300 m

→ a + b + c = 300 m

Where, a, b and c are the sides of a triangular park.

So,

→ 2x + 6x + 7x = 300 m

→ 8x + 7x = 300 m

→ 15x = 300 m

→ x = 300/15 m

→ x = 20 m

So, the sides of a triangular park :

The first side = 2x = 2 × 20 m = 40 m.

The second side = 6x = 6 × 20 m = 120 m.

The third side = 7x = 7 × 20 m = 140 m.

Now, we have to find the area of a triangular park.

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★ NOTE → After this step the solution is in the attachment :) It's my own Word :)