Parallelogram PARL is similar to parallelogram WXYZ. If AP = 18, PL = 24, and WZ = 96, find the value of c.
To find the value of c, we need to determine the scale factor between the two similar parallelograms. The scale factor can be found by comparing the corresponding sides of the two parallelograms.
In this case, we can compare the lengths of PA and WZ.
The equation for the scale factor is:
scale factor = length of corresponding side in PARL / length of corresponding side in WXYZ
Therefore,
scale factor = PA / WZ
Given that PA = 18 and WZ = 96:
scale factor = 18 / 96
To find the value of c, we need to find the length of side XY in parallelogram WXYZ. Since the parallelograms are similar, the corresponding sides are proportional. We can use the scale factor to find the length of XY.
Therefore,
XY = scale factor * PL
Given that PL = 24:
XY = (18 / 96) * 24
Now, calculating the value of XY:
XY = (3 / 16) * 24
XY = 72 / 16
XY = 4.5
Hence, the value of c is 4.5.
To solve this problem, we can use the concept of similarity of triangles and the properties of similar figures.
First, let's identify the corresponding sides of the parallelograms:
- In parallelogram PARL, we are given AP = 18 and PL = 24.
- In parallelogram WXYZ, we are given WZ = 96.
Since the parallelograms are similar, the corresponding sides are proportional. We can set up the following proportion:
AP/WZ = PL/c
Substituting the given values, we have:
18/96 = 24/c
To solve for c, we can cross multiply the equation:
18c = 96 * 24
Now, divide both sides by 18 to isolate c:
c = (96 * 24) / 18
Simplifying:
c = 128
Therefore, the value of c is 128.
The answer is 72
c=72
All the sides are in the same ratio.
WZ/PL = 96/24 = 4
So, XW = 4*AP = 4*18 = 72
I have no ides what c is.