# Find the legnths x and y Thanks for your help

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### 1 Answer

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**