Aregular pentagon is dilated by a scale factor of 73 to create a new pentagon. how does the perimeter of the new pentagon compare with the original perimeter?

Question:

A regular pentagon is dilated by a scale factor of 7/3 to create a new pentagon. How does the perimeter of the new pentagon compare with the original perimeter?

The perimeter of the new pentagon is equal to times the perimeter of the original pentagon

Solution:

If two figures are similar, then the ratio of its perimeters is equal to the scale factor

Let ,

z is the scale factor

x is the perimeter of the new pentagon

y is the perimeter of the original pentagon

Then,

Scale factor = ratio of perimeters

In this problem we have

Substituting we get,

Which means,

Therefore , the perimeter of the new pentagon is equal to times the perimeter of the original pentagon

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3