Parallelogram PARL is similar to parallelogram WXYZ. If AP = 16, PL = 24, and WZ = 96, find the value of c.
Where does c possibly enter the story????
Assuming you followed convention and labelled the parallelograms
using corresponding sides, the only side we can really find is WX
WX/96 = 16/24
WX = 96(16/24) = .....
To find the value of c, we first need to understand the concept of similar polygons. Similar polygons have the same shape, but their sizes may be different.
In this case, we are given that parallelogram PARL is similar to parallelogram WXYZ. This means that corresponding angles between the two parallelograms are equal, and corresponding sides are proportional.
Let's denote the length of side PA as a, and the length of side WX as b. Since the sides of similar polygons are proportional, we can write the following ratios:
PA/WX = PL/WZ
Substituting the given values, we get:
16/96 = 24/c
To find the value of c, we can cross-multiply and solve for c:
16c = 24 * 96
Now, divide both sides by 16 to solve for c:
c = (24 * 96) / 16
Simplifying the right side, we have:
c = 6 * 96
c = 576
Therefore, the value of c is 576.
To solve this problem, we need to use the property of similar figures, which states that corresponding sides of similar figures are proportional.
In parallelogram PARL, the corresponding side to WZ is PL.
So, we can write the proportion as follows:
PL/WZ = AP/XY
Let's substitute the given values:
24/96 = 16/XY
To find the value of XY, we can cross-multiply and solve for it:
(24)(XY) = (16)(96)
24XY = 1536
Now, solve for XY by dividing both sides of the equation by 24:
XY = 1536/24
XY = 64
Therefore, the value of c is 64.