Respuesta :
The new perimeter is ONE FOURTH the original perimeter.
The new area is one sixteenth the original area.
Step-by-step explanation:
Here, the three sides of the triangle are:
A = 16 cm, B = 34 and C = 30 cm
Now, each side of the triangle is divided by 4.
So, the new sides A', B' and C' are:
[tex]A' = (\frac{A}{4}), B' = (\frac{B}{4}) , C' = (\frac{C}{4})[/tex]
The perimeter of the triangle = SUM OF ALL SIDES
⇒ Perimeter (P) = A + B +C ........ (1)
So, the new perimeter (P') = A' + B' + C' = [tex](\frac{A}{4} ) + (\frac{B}{4} )+ (\frac{C}{4} ) = (\frac{A+B+ C}{4} ) = \frac{P}{4}[/tex]
⇒P' = P/4
So, the new perimeter is ONE FOURTH the original perimeter.
Area of the triangle = [tex]\frac{1}{2} \times B \times H[/tex]
Now, the Area(Area) = [tex]\frac{1}{2} \times A \times B = \frac{AB}{2}[/tex]
The new area A' = [tex]\frac{1}{2} \times (\frac{A'}{4}) \times (\frac{B'}{4}) = \frac{A'B'}{16\times 2} = \frac{Area}{16}[/tex]
So, the new area A' is one sixteenth the original area.
