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

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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.**

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.**

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