Question

You can use similar triangles to find the height of a tree. Triangle ABC is similar to triangle DEC. What is the height of the tree?

Equations and inequalities
ANSWERED
asked 2021-02-02
You can use similar triangles to find the height of a tree. Triangle ABC is similar to triangle DEC. What is the height of the tree?

Answers (1)

2021-02-03
The height of the tree is x feet based on the diagram.
Similar triangles have side lengths that are proportional so we can write:
\(\displaystyle{\frac{{{A}{B}}}{{{D}{E}}}}={\frac{{{B}{C}}}{{{E}{C}}}}\)
\(\displaystyle{\frac{{{x}}}{{{4}}}}={\frac{{{9}+{6}}}{{{6}}}}\)
\(\displaystyle{\frac{{{x}}}{{{4}}}}={\frac{{{15}}}{{{6}}}}\)
\(\displaystyle{x}={\frac{{{15}}}{{{6}}}}{\left({4}\right)}\)
\(\displaystyle{x}={10}\)
So, the height of a tree is 10 ft.
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