Answer:
Option B. [tex]XY=15\ in[/tex]
Step-by-step explanation:
step 1
Find the scale factor
we know that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
Let
z----> the scale factor
x----> area of the larger pentagon (UVWXY)
y----> area of the smaller pentagon (LMNPO)
[tex]z^{2}=\frac{x}{y}[/tex]
we have
[tex]x=198\ in^{2}[/tex]
[tex]y=88\ in^{2}[/tex]
substitute
[tex]z^{2}=\frac{198}{88}[/tex]
[tex]z^{2}=2.25[/tex]
[tex]z=1.5[/tex]
step 2
Find XY
we know that
If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor
Let
z----> the scale factor
x----> side XY of the larger pentagon (UVWXY)
y----> side OP of the smaller pentagon (LMNPO)
[tex]z=\frac{x}{y}[/tex]
we have
[tex]z=1.5[/tex]
[tex]y=10\ in[/tex]
substitute
[tex]1.5=\frac{x}{10}[/tex]
[tex]x=1.5*10=15\ in[/tex]
therefore
[tex]XY=15\ in[/tex]
