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A triangle has sides 3, 4 and 5. Find the area of the triangle using 2 methods

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lxsptter | Student, Undergraduate | Valedictorian

Posted February 18, 2012 at 1:24 PM via web

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A triangle has sides 3, 4 and 5. Find the area of the triangle using 2 methods

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted February 18, 2012 at 1:31 PM (Answer #1)

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The area of a triangle with sides 3, 4 and 5 has to be determined using two methods.

It is seen that 3^2 + 4^2 = 9 + 16 = 25 = 5^2

The given triangle is a right-angled triangle. The area of the triangle can be derived using the formula A = `(1/2)*b*h`

=> `(1/2)*3*4`

=> 6

Another way to determine the area is to use Heron's formula.

The semi-perimeter of the triangle is `(3 + 4 + 5)/2 = 6`

The area of the triangle is given by `sqrt(6*(6-3)(6-4)(6-5))`

=> `sqrt(6*3*2*1)`

=> `sqrt 36`

=> 6

Using both the methods the area of the triangle with sides 3, 4 and 5 is 6 square units.

Sources:

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anveshanushka | Student , Undergraduate | Salutatorian

Posted February 18, 2012 at 2:26 PM (Answer #2)

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we see tht this triangle is a right angled triangle.....

thus by using the formula.....

Area = (1/2)*width*height

= (1/2)*3*4

=6

using herons formula......

area= (s*(s-a)*(s-b)*(s-c))^(1/2)   (where s is the semi-perimeter)

(and a,b,c are the sides)

s=(3+4+5)/2

=6

thus area =(6*(6-3)*(6-4)*(6-5))^(1/2)

=36^1/2

=6

..................answer

 

 

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