Question

29
quadrilateral abcd was dilated to make quadrilateral abcd.
(there are two quadrilateral figures, the left one is abcd with side lengths: ab=8 in, bc=3 in, cd=5 in, da=4 in; the right one is abcd with ab=44 in)
what is the length of side cd of the bigger quadrilateral? (note: the quadrilaterals are not drawn to scale.)
a 20 inches
b 27.5 inches
c 22 inches
d 16.5 inches

Explanation:

Step1: Find dilation scale factor

Identify corresponding sides $AB$ and $A'B'$. The scale factor $k = \frac{A'B'}{AB} = \frac{44}{8} = 5.5$

Step2: Calculate length of $C'D'$

Multiply original side $CD$ by scale factor $k$.
$C'D' = CD \times k = 5 \times 5.5$

Answer:

B. 27.5 inches