The polygons shown are similar. Solve for y. They are not drawn to scale. Please show ALL work in order to receive full credit.
x-1
6
16
y+1
12
21
32
24
To solve for y, we need to set up a proportion using the corresponding sides of the two similar polygons.
The corresponding sides are:
x-1 and 6
y+1 and 12
Setting up the proportion:
(x-1)/6 = (y+1)/12
Cross multiplying gives us:
12(x-1) = 6(y+1)
Expanding both sides gives us:
12x - 12 = 6y + 6
Now, solve for y:
12x - 12 = 6y + 6
12x - 12 - 6 = 6y
12x - 18 = 6y
6y = 12x - 18
y = (12x - 18)/6
y = 2x - 3
Therefore, the solution for y is 2x - 3.