Question

if each side of triangle become 1 third....whta is the pecent decease in its area????

Answer 1

Answer:

Let us consider all the sides of the triangle = 3 cm.

Then, Area of the triangle = 1/2*3*3   (that is, 1/2*base* heigth)

                                           = 1/2*9

                                            = 4.5 cm

So, according to the question, each each side of the triangle become one by third then the value of one side = 1/3*3 cm

                                                     = 1 cm

Then the area of the triangle = 1/2*1*1

                                                  = 0.5 cm

So, the percentage decrease in area = actual area of triangle x 100

                                                                  area when side is 1/3

                                                               = 4.5/0.5 *100

                                                               = 9%

                                                               

               

Answer 2

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Area of triangle = A = square root of [s(s-a)(s-b)(s-c) where 2s =a+b+c.

Each side is halved,

s’ = s/2

(s’-a’) = (s-a)/2.

s’-b’) = (s-b)/2.

s’-c’) = (s-c)/2.

New areaA’ = square root of [s(s-a)(s-b)(s-c) /16. = A/ 4.

Change in area = 3/4 A= 75% decrease

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