triangle abc is similar to triangle def and has a ratio 8/10 = 16/20 = 4x+6/4x+11
side ac= ?
well, just plug it in:
(4x+6)/(4x+11) = 8/10
10(4x+6) = 8(4x+11)
40x+60 = 32x+88
8x=28
x = 7/2
I have no idea what side ac is, but its ratio to df is 4/5
To find the length of side AC, we can use the fact that corresponding sides of similar triangles are proportional.
In this case, the ratio of side AB to side DE is given as 8/10 = 16/20 = (4x + 6)/(4x + 11).
We can set up the proportion:
8/10 = (4x + 6)/(4x + 11)
To solve for x, we can cross-multiply:
8(4x + 11) = 10(4x + 6)
Expand both sides:
32x + 88 = 40x + 60
Subtract 32x and 60 from both sides:
40x - 32x = 88 - 60
8x = 28
Divide both sides by 8:
x = 28/8
Simplify:
x = 7/2
Now that we have the value of x, we can find the length of side AC.
Plug in the value of x into the ratio:
AC = 4x + 11 = 4(7/2) + 11 = 14 + 11 = 25
Therefore, the length of side AC is 25.