Question

5. Sides of a triangle are In the ratio 12:17:25 and its perimeter is 540cm find it's area
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Answer 1

Given:-

• Ratio of the sides of the triangle = 12:17:25
• Perimeter = 540

To Find:-

• Area of the triangle

Assumption:-

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

Solution:-

We know,

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 = 120 cm
• 2nd side = 17x = 17 × 10 = 170 cm
• 3rd side = 25x = 25 × 10 = 250 cm

∴ The sides of the triangle are as follows:-

• 1st side = 120 cm
• 2nd side = 170 cm
• 3rd side = 250 cm

Now,

For area,

Let us find the semi-perimeter of the triangle,

We know,

• 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.

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Answer 2

Answer:-

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Given:

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▪︎Sides of triangle in the ratio 12:17:25

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▪︎Perimeter of triangle = 540cm

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To Find:

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▪︎Area of triangle

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Solution:

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➥ Finding measure of sides of triangle

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Let the sides of triangle be 12x , 17x and 25 x

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According to given conditions;

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Perimeter of triangle = 540 cm

➨ Sum of sides = 540 cm

➨ 12x + 17x + 25x = 540 cm

➨ 54x = 540 cm

➨ x = 540 ÷ 54

➨ x = 10cm

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∴ Measure of first side = 12 × 10 = 120cm

∴ Measure of second side = 17 × 10 = 170cm

∴ Measure of third side = 25 × 10 = 250cm

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➥ Finding area of triangle

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Here,

a = first side = 120cm

b = second side = 170cm

c = third side = 250cm

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Value of s

= ( Sum of all sides ) ÷ 2

= 540 ÷ 2

= 270

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Area of triangle by Heron's formula

= $\sf{}\sqrt{s(s-a)(s-b)(s-c)}$

= $\sf{}\sqrt{270(270-120)(270-170)(270-250)}$

= $\sf{}\sqrt{9× 3 × 10 × 3 × 5 × 10 × 10×10×2×10}$

= $\sf{}3 × 3 × 10 × 5 × 2 × 10$

= $\sf{}9000$ cm²

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∴Area of triangle is 9000 cm².