Question

Sides of a triangle are in the ratio of 3: 5: 7 and its semi perimeter is 60 cm. Find its area.

Answer 1

Answer:

The Area of the Triangle is $240\sqrt{3}$ cm².

Step-by-step explanation:

Given:-

• Sides of the triangle are in the ratio of 3: 5: 7 .

• Its semi perimeter is 60 cm.

∴ The perimeter of the Triangle will be=60×2=120 cm.

To Find:-

The area of the Triangle.

Things to Remember:-

In geometry, the semi-perimeter of a Triangle is half of its perimeter.

Formula Applied:-

Perimeter of Triangle= Sum of all of its Sides.

Solution:-

Let the sides of the Triangle be 3x, 5x and 7x.

Now, We know that

Perimeter of Triangle = Sum of all of its Sides

⇒120=3x+5x+7x

⇒120=15x

⇒$x=\frac{120}{15} cm$

⇒ x= 8 cm

∴ The sides of the triangle will be 24 cm, 40 cm, 56 cm.

S=$\frac{a+b+c}{2}$=$\frac{120}{2}$=60 cm

Area of the Triangle

⇒$\sqrt{s\times(s-a)\times(s-b)\times(s-c)}$ where a=24, b=40, c=56

⇒$\sqrt{60\times(60-24)\times(60-40)\times(60-56)}$

⇒$\sqrt{60\times36\times20\times4}$

⇒ $10\times2\times6\times2\sqrt{3}$

⇒$240\sqrt{3}$ cm²

Answer 2

Step-by-step explanation:

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