Parallelogram PARL is similar to parallelogram WXYZ. If AP = 16, PL = 24, and WZ = 96, find the value of c.
HELP PLEASE!! <3
No idea where c enters the picture , but ...
WX/96 = 16/24
WX = (16/24)(96) = ....
Since in a parallelogram opposite sides are equal you now know them all
To find the value of c, we need to compare corresponding side lengths of the similar parallelograms.
First, let's label the corresponding side lengths:
AP = 16
PL = 24
If the corresponding side in parallelogram PARL is AP and its length is 16, the corresponding side in parallelogram WXYZ would be WX (since A corresponds to W, and P corresponds to X).
Similarly, if the corresponding side in parallelogram PARL is PL and its length is 24, the corresponding side in parallelogram WXYZ would be YZ (since L corresponds to Y, and P corresponds to Z).
Since the parallelograms are similar, we can set up a proportion using the corresponding side lengths:
AP/WX = PL/YZ
Substituting the given values:
16/WX = 24/YZ
Now, we can calculate the value of WX using cross multiplication:
16 * YZ = 24 * WX
The corresponding sides WX and YZ have lengths 96 and c (unknown), respectively.
Substituting these values into the equation:
16 * c = 24 * 96
Now we can solve for c:
16c = 2304
Dividing both sides by 16:
c = 2304/16
Simplifying:
c = 144
Therefore, the value of c is 144.
To find the value of c, we need to determine the relationship between the corresponding sides of similar figures.
In similar figures, the corresponding sides are proportional. Since we are given that parallelogram PARL is similar to parallelogram WXYZ, we can set up a proportion:
AP/WZ = PL/c
Substituting the given values, we have:
16/96 = 24/c
Now, we can solve for c.
To do that, we can cross-multiply and then solve for c:
16c = 96 * 24
Next, divide both sides of the equation by 16 to isolate c:
c = (96 * 24) / 16
Now calculate the value of c:
c = 144
Therefore, the value of c is 144.