Answer:
The scale factor used to go from P to Q is 1/4
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
If two figures are similar, then the ratio of its areas i equal to the scale factor squared
Let
z ----> the scale factor
x -----> area of polygon Q
y -----> area of polygon P
[tex]z^{2}=\frac{x}{y}[/tex]
we have
[tex]y=72\ units^2[/tex]
Find the area of polygon Q
Divide the the area of polygon Q in two triangles and three squares
The area of the polygon Q is equal to the area of two triangles plus the area of three squares
see the attached figure N 2
Find the area of triangle 1
[tex]A=(1/2)(1)(2)=1\ units^2[/tex]
Find the area of three squares (A2,A3 and A4)
[tex]A=3(1)^2=3\ units^2[/tex]
Find the area of triangle 5
[tex]A=(1/2)(1)(1)=0.5\ units^2[/tex]
The area of polygon Q is
[tex]x=1+3+0.5=4.5\ units^2[/tex]
Find the scale factor
[tex]z^{2}=\frac{x}{y}[/tex]
we have
[tex]y=72\ units^2[/tex]
[tex]x=4.5\ units^2[/tex]
substitute and solve for z
[tex]z^{2}=\frac{4.5}{72}[/tex]
[tex]z^{2}=\frac{1}{16}[/tex]
square root both sides
[tex]z=\frac{1}{4}[/tex]
therefore
The scale factor used to go from P to Q is 1/4
The scaled factor did Diego used to go from P to Q is 1/4.
Given
The area of polygon P is 72 square units.
If two figures are similar, then the ratio of its areas is equal to the scale factor squared.
[tex]\rm z^2=\dfrac{x}{y}[/tex]
Where; z is the scale factor, x = area of polygon Q, y = area of polygon P.
Therefore,
The area of the first triangle is;
[tex]\rm Area = \dfrac{1}{2} \times base \times height\\\\Area = \dfrac{1}{2} \times 1 \times 2\\\\Area = 1 \ units[/tex]
The area of three squares (A2, A3, and A4)
[tex]\rm Area = 3(1)^2\\\\Area = 3\ square \ units[/tex]
The area of the 5th triangle is;
[tex]\rm Area = \dfrac{1}{2} \times base \times height\\\\Area = \dfrac{1}{2} \times 1 \times 1\\\\Area = 0.5 \ units[/tex]
Then,
The area of the polygon is;
x = 1 + 3 + 0.5 = 4.5 units
Therefore,
The scaled factor did Diego used to go from P to Q is;
[tex]\rm z^2=\dfrac{4.5}{72}\\\\z^2=\dfrac{1}{16}\\\\z=\dfrac{1}{4}\\\\[/tex]
Hence, the scaled factor did Diego used to go from P to Q is 1/4.
To know more about the Scale factor click the link given below.
https://brainly.com/question/22644306
