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6). Sides of a triangles are in the ratio of 12:17:25 and it's perimeter is 540cm. Find it's area using heron's formula

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Answer 1

Given :

• Sides of a triangles are in the ratio of 12:17:25.
• And it's perimeter is 540 cm.

To Find :

• Find are of the triangle ?

Assumption :

• Let the ratio common be x.
• 1st side = 12x
• 2nd side = 17x
• 3rd side = 25x

Solution :

We know that,

• Perimeter of a triangle = 1st side + 2nd side + 3rd side

Hence,

• 540 = 12x + 17x + 25x

➣ 54x = 540

➣ x = 540/54

➣ x = 10

Putting the value of x in the sides :

• 1st side = 12x = 12 × 10 = 20 cm
• 2nd side = 17x = 17 × 10 = 70 cm
• 3rd side = 25x = 25 × 10 = 250 cm

The sides of the triangle are as follows :

• 1st = 20 cm
• 2nd = 70 cm
• 3rd = 250 cm

We know that,

• s = (a + b + c)/2

therefore,

➣ s = (120 + 170 + 250)/2

➣ s = 540/2

➣ s = 270

According to Heron's formula,

• A = √s(s - a)(s - b)(s - c)

Hence,

Area = √270(270 - 120)(270 - 170)(270 -250)

Area = √270 × 150 × 100 × 20

Area = √81000000

Area = 9000 cm²

• Area of the triangle is 9000 cm².