Find the legnths x and y     Thanks for your help

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Expert Answers
samhouston eNotes educator| Certified Educator

This problem can be solved using laws of similar triangles.  The ratios of corresponding sides of similar triangles are equal.  This also includes corresponding segments in similar triangles.

To find x:

Step 1:  Write equal ratios as a proportion.

AG / AF = BC / BD
14 / (14 + 21) = x / (x + 15)
14 / 35 = x / (x + 15)

Step 2:  Solve the proportion by cross-multiplying.

14 * (x + 15) = 35 * x
14x + 210 = 35x
14x + 210 + (-14x) = 35x + (-14x)
210 = 21x
210 / 21 = 21x / 21
x  = 10

To find y:

Step 1:  Write equal ratios as a proportion.

FE / AE  = DE / BE 
y / (14 + 21 + y) = 20 / (10 + 15 + 20)
y / (35 + y) = 20 / 45

Step 2:  Solve the proportion by cross-multiplying.

45 * y = 20 * (35 + y) 
45y = 700 + 20y
45y + (-20y) = 700 + 20y + (-20y)
25y = 700
25y / 25 = 700 / 25
y = 28

Final answer:
x = 10
y = 28