Ms. O'Brien is decorating a bulletin board in her classroom. She started with a regular pentagon in the top left corner of the board but then decided to move the pentagon to the bottom right hand corner, as shown below.
If the base of the pentagon measured 15 cm when it was placed in the top left corner, what will the base of the pentagon measure when placed in the bottom right corner?
Since Ms. O'Brien moved the pentagon from the top left corner to the bottom right corner, the base of the pentagon will remain the same length. Therefore, the base of the pentagon will still measure 15 cm when placed in the bottom right corner.
To find the new base measurement of the pentagon when placed in the bottom right corner, we can use the concept of similar triangles.
Since the pentagon is moved from the top left corner to the bottom right corner, it undergoes a translation but does not change shape or size. Therefore, the two pentagons are similar.
Let's denote the original pentagon's base measurement as b1 and the new pentagon's base measurement as b2.
Using the concept of similar triangles, we can set up a proportion between the base and corresponding sides of the pentagon:
b1 / x1 = b2 / x2
Here, x1 and x2 represent the corresponding side lengths of the pentagon in the top left and bottom right corner, respectively.
Since we are only interested in finding the new base measurement, the x-values are not important for this calculation. Thus, we can set x1 = x2 = 1.
Plugging in the given information, we have:
15 / 1 = b2 / 1
Multiply both sides by 1 to isolate b2:
15 = b2
Therefore, the base of the pentagon will measure 15 cm when placed in the bottom right corner.
To find the length of the base of the pentagon when it is placed in the bottom right corner, we need to understand the transformation that occurred. Since the base of the pentagon measures 15 cm in the top left corner, the length of the base remains the same.
The movement of the pentagon from the top left corner to the bottom right corner does not affect the length of its base. Therefore, the base of the pentagon will still measure 15 cm when placed in the bottom right corner.