Parallelogram PARL is similar to parallelogram WXYZ. If AP= 15, PL=25, and WZ= 75, Find the value of c.
A. 75
B. 40
C. 45
D. 3
There is no answer choice with 125.
In similar polygons, corresponding sides are proportional. Therefore, we can set up the following proportion:
\(\frac{AP}{WZ} = \frac{PL}{YZ}\)
\(\frac{15}{75} = \frac{25}{YZ}\)
Cross multiplying, we get:
\(25 \cdot 75 = 15 \cdot YZ\)
\(1875 = 15 \cdot YZ\)
\(YZ = \frac{1875}{15}\)
\(YZ = 125\)
Since \(YZ = 125\) and \(PL = 25\), we can find the value of c by subtracting these two side lengths:
\(c = YZ - PL = 125 - 25 = 100\)
None of the answer choices provided match the value of 100.