1.

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

Answer»

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


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