Question

Solve for the unknown length.

Answer 1

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:

• $\dfrac{a}{b}=\dfrac{h}{k}$

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?).

• Triangle ABC
• Triangle ADE

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:

$\dfrac{x}{15}=\dfrac{50}{20}\\\\\dfrac{x}{15}=\dfrac{5}{2}\\\\x=\dfrac{5}{2}*15\\\\x=\dfrac{75}{2}\\\\x=37.5$

Therefore, the unknown length is 37.5 units.

Answer

37.5 units