Question

if the side of an equilateral triangle are tripled. then find its area .by using herons formula.​

Answer 1

Answer:

9 times of original

Step-by-step explanation:

Consider a triangle of side-length 2a.

  Semi-perimeter = ( 2a + 2a + 2a ) / 2 = 3a

Using Heron's formula:

⇒ √[ 3a( 3a - 2a )( 3a - 2a )( 3a - 2a )]

⇒ √[ 3a*a*a*a ]

⇒ a²√3

    When sides are tripled: new sides are 6a, 6a, 6a( triple of 2a ).

 Semi - perimeter = ( 6a + 6a + 6a ) / 2 = 9a

using heron's formula:

⇒ √[ 9a( 9a - 6a )( 9a - 6a )( 9a - 6a )]

⇒ √( 9a * 3a * 3a * 3a )

⇒ a²√( 3^2 * 3 * 3^2 )

⇒ 3*3*a²√3

⇒ 3*3 * a²√3

⇒ 9 * a²√3

   Hence the new area is 9 times of the original one.

Answer 2

Answer:

Please see the attachment below.

This answer is for class 10

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