Question

Similarity of triangles. Find x

Similarity
ANSWERED
asked 2021-08-10
Similarity of triangles. Find x
image

Answers (1)

2021-08-11

Since \(\displaystyle\angle{C}{D}{E}=\angle{A}{B}{E}={0},{D}{C}\parallel{A}{B}\).
Hence, \(\displaystyle\angle{D}{C}{E}=\angle{E}{A}{B}\).
Also \(\displaystyle\angle{D}{E}{C}=\angle{A}{E}{B}\) (opposite angle).
Hence \(\displaystyle\triangle{D}{C}{E}\sim\triangle{A}{E}{B}\).
So \(\displaystyle{\frac{{{A}{B}}}{{{D}{C}}}}={\frac{{{B}{E}}}{{{E}{D}}}}\)
or \(\displaystyle{\frac{{{21}}}{{{x}}}}={\frac{{{14}}}{{{8}}}}={\frac{{{7}}}{{{4}}}}\)
or \(\displaystyle{x}={\frac{{{21}\times{4}}}{{{7}}}}={\frac{{{3}\times{7}\times{4}}}{{{7}}}}={12}\)
\(\displaystyle\therefore{x}={12}\)

0
 
Best answer

expert advice

Have a similar question?
We can deal with it in 3 hours
...