Consider the following figure where \triangle ABC \sim \triangle DBE AC=16, CB=10

abondantQ 2021-08-11 Answered
Consider the following figure where \(\displaystyle\triangle{A}{B}{C}\sim\triangle{D}{B}{E}\).
image
Given: AC=16, CB=10
E is the midpoint of \(\displaystyle\overline{{{C}{B}}}\)
Find: DE

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Expert Answer

crocolylec
Answered 2021-08-12 Author has 18750 answers
Step 1
Explanation:
Given that,
\(\displaystyle\triangle{A}{B}{C}\sim\triangle{D}{B}{E}\)
AC=16
CB=10
E is the midpoint of CB
E is the midpoint, it means
BE=EC=5
We need to find the DE
Step 2
According to the triangle's similarity, the corresponding ratio of sides is the same.
\(\displaystyle{\frac{{{D}{E}}}{{{A}{C}}}}={\frac{{{B}{E}}}{{{C}{B}}}}\)
Suppose DE=x
So,
\(\displaystyle{\frac{{{x}}}{{{16}}}}={\frac{{{5}}}{{{10}}}}\)
\(\displaystyle{x}={\frac{{{5}}}{{{10}}}}\times{16}\)
x=8
Hence, the DE=8
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