## The sides of a triangle are in the ratio 3:57I and its perimeter is 600m find the area oftriangle​

Question

The sides of a triangle are in the ratio 3:57
I and its perimeter is 600m find the area of
triangle​

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1 month 2021-08-16T06:41:16+00:00 2 Answers 0 views 0

1. Appropriate Question :

• The Sides of Triangle are in the ratio 3:5:7 and it’s Perimeter is 600 m . Find the Area of Triangle .

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Given : The Sides of Triangle are in the ratio 3:5:7 & Perimeter of Triangle is 600 m .

Exigency to find : Area of Triangle .

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❍ Let’s Consider the three sides of Triangle be 3x , 5x & 7x .

⠀⠀⠀⠀⠀Finding Three Sides of Triangle :  ⠀⠀⠀⠀⠀Here a , b & c are three sides of Triangle & we know that Perimeter of Triangle is 400 m .

⠀⠀⠀⠀⠀⠀      Therefore,

• a or First Side is 3x = 3(40) = 120 m
• b or Second Side is 5x = 5(40) = 200 m
• c or Third side is 7x = 7(40) = 280 m

Therefore,

⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀ Finding Semi-Perimeter of Triangle for Finding Area of Triangle :  ⠀⠀⠀⠀⠀Here Perimeter of Triangle is 600 m .

⠀⠀⠀⠀⠀⠀    Therefore,

⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

⠀⠀⠀⠀⠀ Finding Area of Triangle :  ⠀⠀⠀⠀⠀Here a , b & c are three sides of Triangle & s is the Semi-Perimeter of Triangle.

⠀⠀⠀⠀⠀⠀        Therefore,

⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

2. Given:

• The sides of a triangle are in the ratio 3:5:7
• Perimeter of the triangle is 600m.

To find:

• Area of triangle?

Solution:

• Let’s consider ABC is a triangle.

Where,

• A = 3x
• B = 5x
• C = 7x

• Let angle in common be x.

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« Now, By using perimeter of triangle formula,

Perimeter of triangle = a + b + c

→ 3x + 5x + 7x = 600

→ 15x = 600

→ x = 600/15

→ x = 40

Thus, The sides of the triangle are 120m,200m & 280m.

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« Now, Let’s Find Area of triangle by using herons formula,

As we know that,

√s(sa)(sb)(sc)

• Side = 120 + 200 + 280/2 = 300

→ √300(300 – 120)(300 – 200)(300 – 280)

→ √300(180)(100)(20)

→ √300(360000)

→ √108000000

→ 6000√3

∴ Hence, Area of of the triangle is 6000√3.