Question

if each side of a triangle is halved , then its perimeter will be decreased by what per cent ?

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%

hope it helps .....

Answer 2

Answer:

75% decrease

Step-by-step explanation:

let the sides of the triangle be x y & z

their semi-perimeter or s = (x+y+z)/2

let the sides of the new triangle be x/2 y/2 & z/2

their semi-perimeter or s' = (x/2+y/2+z/2)/2

                                  =(x+y+z)/2/2

                                  = (x+y=z)/4

s' = s/2

area of the normal triangle or a = √s(s-x)(s-y)(s-z)

area of new triangle or a' = √s/2(s/2-x/2)(s/2-y/2)(s/2-z/2)

                                          = √s/2(s-x)/2(s-y)/2(s-z)/2

                                          =√(s(s-x)(s-y)(s-z))/16

                                          =a√1/16

                                          = a/4

percentage decrease = 100-((new/old) x 100)

                                    = 100-(((a/4)/a) x 100)

                                    =100-(1/4 x 100)

                                    =100-25

                                    = 75%