3. Diego drew a scaled version of a Polygon P and labeled it Q.If the area of Polygon P is 72 square units, what scale factordid Diego use to go from P to Q? Explain your reasoning. PLEASE ANSWER QUICKLY ​

Answer:The scale factor used to go from P to Q is 1/4Step-by-step explanation:see the attached figure to better understand the problemwe know thatIf two figures are similar, then the ratio of its areas is equal to the scale factor squaredLetz ----> the scale factorx -----> area of polygon Qy -----> area of polygon P[tex]z^{2}=\frac{x}{y}[/tex]we have[tex]y=72\ units^2[/tex]Find the area of polygon QDivide the the area of polygon Q in two triangles and three squaresThe area of the polygon Q is equal to the area of two triangles plus the area of three squaressee the attached figure N 2Find 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]thereforeThe scale factor used to go from P to Q is 1/4