Question

If each side of the triangle is halved then what will be the effect on its perimeter and by what percentage

Answer 1

Triangle EAD is the triangle obtained by bisecting each side of a given triangle ABC.

Here, ratio of the length of the sides of new triangle to the length of the corresponding sides of original triangle = 1:2

And triangle CDE ~ triangle ABC ( by AAA Similarity criterion)

So, area ( triangleCDE) : area( triangle ABC)

= 1 : 4 ( by area similarity theorem , which states that ratio of the areas of 2 similar triangles is equal to the square of their corresponding sides

So, If area of smaller triangle is x then the area of larger triangle = 4x

Decrease in area 4x -x =3x

So, percentage decrease

= ( decrease in area/ Original area) * 100

= (3x / 4x)*100

= 75%