Question

Triangle dimensions are 16, 34 and 30 meters. Suppose the side lenghts and height of triangle were divided by 4. What effect would this have on the perimeter? The area?

Answer 1

The new perimeter is ONE FOURTH the original perimeter.

The new area is one sixteenth the original area.

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:

`A' = ((A)/(4)), B' = ((B)/(4)) , C' = ((C)/(4))`

The perimeter of the triangle = SUM OF ALL SIDES

⇒ Perimeter (P) = A + B +C ........ (1)

So, the new perimeter (P') = A' + B' + C' =
`((A)/(4) ) + ((B)/(4) )+ ((C)/(4) ) = ((A+B+ C)/(4) ) = (P)/(4)`

⇒P' = P/4

So, the new perimeter is ONE FOURTH the original perimeter.

Area of the triangle =
`(1)/(2) * B * H`

Now, the Area(Area) =
`(1)/(2) * A * B = (AB)/(2)`

The new area A' =
`(1)/(2) * ((A')/(4)) * ((B')/(4)) = (A'B')/(16* 2) = (Area)/(16)`

So, the new area A' is one sixteenth the original area.