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
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?

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.