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Question
Math
Posted 2 months ago

Triangle DEFD E F is similar to triangle ABCA B C.
Solve for yy.
y=
y=
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Answer from Sia
Posted 2 months ago
Solution by Steps
step 1
Given that triangles DEFDEF and ABCABC are similar, we can set up a proportion using corresponding sides
step 2
The proportion based on the similarity is DEBC=DFBA\frac{DE}{BC} = \frac{DF}{BA}. Substituting the given lengths, we get 37.516.5=20y\frac{37.5}{16.5} = \frac{20}{y}
step 3
To solve for yy, cross-multiply to get 37.5y=16.5×2037.5y = 16.5 \times 20
step 4
Simplify the equation to find yy by dividing both sides by 37.5, resulting in y=16.5×2037.5y = \frac{16.5 \times 20}{37.5}
step 5
Calculate the value of yy to get y=33037.5y = \frac{330}{37.5}
step 6
Simplify the fraction to get y=445y = \frac{44}{5} or y=8.8y = 8.8
Answer
y=445y = \frac{44}{5} or y=8.8y = 8.8
Key Concept
Similar Triangles and Proportions
Explanation
When two triangles are similar, the ratios of the lengths of their corresponding sides are equal. This property is used to solve for unknown sides.

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