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