Question

sides of a triangle are in the ratio 12:17:25 and its perimeter is 540 find its area​

Answer 1

• Area of triangle is 9000.

Explanation:

Given:-

• Sides of triangle are in ratio 12:17:25 .
• Perimeter of triangle is 540.

To find:-

• Area of triangle.

Solution:-

Let, Sides of triangle by 12x, 17x and 25x.

Perimeter of triangle = a + b + c

In which,

• a, b and c are sides of triangle.

So,

➝ 12x + 17x + 25x = 540

➝ 54x = 540

➝ x = 540/54

➝ x = 10

Sides will be

12x = 12 × 10 = 120

17x = 17 × 10 = 170

25x = 25 × 10 = 250

• We do not have height of triangle. So, we can't use 1/2 × b × h. We will use heron's Formula for area.

We know that,

Formula of heron's formula is :

Area of triangle = √s(s - a)(s - b)(s - c)

In which,

• S is semi-perimeter of triangle.
• a, b and c are sides of triangle.

So,

s = Perimeter/2

s = 540/2

s = 270

Semi-perimeter is 270.

Put s and sides of triangle in formula:

➝ √270 (270 - 120)(270 - 170)(270 - 250)

➝ √270 × 150 × 100 × 20

➝√2×3×3×3×5×2×3×5×5×2×2×5×5×2×2×5

➝ 2 × 2 × 2 × 3 × 3 × 5 × 5 × 5

➝ 9000

Therefore,

Area of triangle is 9000.

Answer 2

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Sides of triangle -

12 : 17 : 25

Perimeter of triangle -

540

Let sides be,

12x , 17x , 25x

So,

12x + 17x + 25x = 540

54x = 540

x = 540

x = 540 / 54

x = 10

So sides,

12x = 12 × 10 = 120

17x = 17 × 10 = 170

25x = 25 × 10 = 250

Using Heron's Formula -

Area = √s(s-a) (s-b) (s-c)

Semi perimeter = Perimeter / 2

Semi perimeter = 540 / 2

Semi perimeter = 270

Then area

√270(270-120) (270-170) (270-250)

√270 × 150 × 100 × 20

√2 × 3× 3 × 3 × 5 × 2 × 3 × 5 × 5 × 2 × 2 × 5 × 5 × 2 × 2 × 5

2 × 2 × 2 × 3 × 3 × 5 × 5

9000

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