Final Answer:
40.375
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Explanation:
- We are told that triangle HYV and triangle AYB are similar. That means their sides match up in the same ratio.
- Look at the sides: In small triangle AYB, side YB is 16. In big triangle HYV, side YV is 16 + 22 = 38.
- So the big triangle is bigger by a factor of 38 ÷ 16.
- Now look at side AY in the small triangle — it’s 17. The matching side in the big triangle is HY, which is x.
- So we set up: x ÷ 17 = 38 ÷ 16
- Multiply both sides by 17: x = (38 ÷ 16) × 17
- Do the math: 38 ÷ 16 = 2.375, then 2.375 × 17 = 40.375
- So x = 40.375
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Parent Tip: Review the logic above to help your child master the concept of triangle similarity theorems worksheet.
