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

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