A pentagon has all sides equal. A rectangle has width twice as long as the side of the pentagon and length four times as long. The perimeter of the rectangle is 30 inches. What is the perimeter of the pentagon?

the perimeter of the Pentagon is 12.5 inches

Step-by-step explanation:

Let x represent the length of each side of the Pentagon.

A rectangle has width twice as long as the side of the pentagon. This means that the width of the rectangle, w is 2x

The rectangle has length four times as long as the side of the pentagon. This means that the length of the rectangle, l is 4x

The formula for determining the perimeter of a rectangle is expressed as

Perimeter = 2(l + w)

The perimeter of the rectangle is 30 inches. This means that

2(2x + 4x) = 30

12x = 30

x = 30/12 = 2.5

A Pentagon has 5 sides. This means that the perimeter of the Pentagon is

5 × 2.5 = 12.5 inches

3.

Step-by-step explanation:

When a figure with vertices (x,y) is dilated from the origin by a scale factor 'k' .

Then , the coordinates of the image is given by :-

Given : Segment AB is dilated from the origin to create segment A prime B prime at A' (0, 6) and B' (6, 9).

From the graph , coordinates of AB are A(0,2) and B(2,3).

Let k be the scale factor then ,

Since A' is the image of point A.

Then,

Hence, the scale factor was 3.