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What happens to the area of a triangle if the lengths of the sides doubled?

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neefo | Student, Undergraduate | eNoter

Posted April 13, 2011 at 11:01 AM via web

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What happens to the area of a triangle if the lengths of the sides doubled?

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted April 13, 2011 at 11:05 AM (Answer #1)

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Let the sides of a triangle be a,b, and c, and let the height be h.

Then We will assume that c is the base and h is the height.

Then the area is given by :

A 1= (1/2) * c * h ...........(1)

Now when the sides doubles, the sides are: 2a, 2b, 2c, and the height is 2h

==> Then the area is given by :

A2 = (1/2)* 2c * 2h  = 4*(1/2)*c * h

But (1/2)*c*h= A1

==> A2 = 4* A1

Then the area of the triangle is increased by a factor of 4 if the sides are doubled.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted April 13, 2011 at 11:08 AM (Answer #2)

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The area of a triangle is given by (1/2)*base*height.

If the length of the sides becomes double so does the height.

As base and height are becoming double the new area is 4 times the original area.

When the length of the sides of a triangle double, the area becomes quadruple.

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tylak | Student, Grade 10 | eNoter

Posted April 13, 2011 at 7:01 PM (Answer #3)

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we have a theorem that,

the ratio of the areas of two similar triangles is equal to the ratio of the squares of any two corresponding sides of a triangle

i.e.,a^2/(2a)^2                                            A  .

=>a^2/4a^2                                            B .__a_.C        

=>1/4                                                    D .___2a___.E             

=>1:4

therefore , thier area of doubled length  triangle is 4 times the actual triangle                               

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