Answer with explanation:
→The Smaller Quadrilateral called image is a dilation of Larger Quadrilateral ,having dilation factor less than 1.
→So,when image has smaller size than preimage,it means
0< Dilation Factor <1
→Also,the Ratio of Corresponding sides,as well as area and perimeter of two Quadrilaterals will be congruent.
Dilation factor
[tex]=\frac{8}{28}\\\\=\frac{2}{7}[/tex]
If 28,x,y and z are length of corresponding sides of larger Quadrilateral,that is pre image then 8, [tex]\frac{2x}{7},\frac{2y}{7},\frac{2z}{7}[/tex] are respectively corresponding side lengths of Image that is Smaller Quadrilateral.
→→Ratio of the perimeter of pre image and Image
[tex]=\frac{28+x+y+z}{8+\frac{2x}{7}+\frac{2y}{7}+\frac{2z}{7}}\\\\=\frac{7\times(28+x+y+z)}{2\times(28+x+y+z)}\\\\=\frac{7}{2}[/tex]
→→Ratio of areas of two Quadrilateral ,that is pre image and Image
=Square of Corresponding Side
[tex]=\frac{28^2}{8^2}\\\\=\frac{784}{64}\\\\=\frac{49}{4}[/tex]
Option B
