The values of the variables a,b, c, d, e, f are 22.8, 15.6, 15, 5, 4 and 8 respectively.
What is similar triangles?
From the figure
Using the concept of similar triangles. The corresponding sides are proportional.
d/12.5 = 10/25
25d = 12.5 * 10
25d = 125
d = 125/25 = 5
f/12 + f = 10/25
25f = 10(12 + f)
25f = 120 + 10f
15f = 120
f = 120/15 = 8
5/c = 10/30
10c = 5 * 30
10c = 150
c = 150/10 = 15
d/c = f/(f + 12 + e)
5/15 = 8/(8 + 12 + e)
1/3 = 8/20 + e
3 * 8 = 20 + e
e = 24 - 20
e = 4
d/a = f/(f + 12 + e + 12.5)
5/a = 8/(8 + 12 + 4 + 12.5)
5/a = 8/36.5
8a = 5 * 36.5
8a = 182.5
a = 182.5/8 = 22.8
d/a = 10/(10 + 15 + 5 + b)
5/22.8 = 10/(30 + b)
5(30 + b) = 10 * 22.8
150 + 5b = 228
5b = 228 - 150
5b = 78
b = 78/5 = 15.6
Therefore, the values of the variables a,b, c, d, e, f are 22.8, 15.6, 15, 5, 4 and 8 respectively.