Similar Triangles
Similar triangles have the same proportions of sides, but they have different side lengths.
To solve for missing sides in similar triangles, we can set up a proportion.
For instance, let's say that side a in Triangle A corresponds with side b in Triangle B. Let's say that side h in Triangle A also corresponds with side k in Triangle B. Then, it would be true that:
- [tex]\dfrac{a}{b}=\dfrac{h}{k}[/tex]
We need to make sure of a couple things:
- The numerators and denominators of fractions are corresponding
- The numerators describe one triangle, and the denominators describe another (can't switch, otherwise the calculations will get messed up)
Solving the Question
We're given two triangles (do you see it?).
These two triangles are similar.
We must solve for the length of side BC in Triangle ABC.
- We're given the length of DE, the corresponding side in Triangle ADE.
- We're also given the lengths of bottom sides, 20 units and 30 + 20 = 50 units.
Set up a proportion:
[tex]\dfrac{x}{15}=\dfrac{50}{20}\\\\\dfrac{x}{15}=\dfrac{5}{2}\\\\x=\dfrac{5}{2}*15\\\\x=\dfrac{75}{2}\\\\x=37.5[/tex]
Therefore, the unknown length is 37.5 units.
Answer
37.5 units
