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koban [17]
2 years ago
11

Solve for the unknown length.

Mathematics
1 answer:
tatyana61 [14]2 years ago
8 0
<h2>Similar Triangles</h2>

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 <em>a</em> in Triangle A corresponds with side <em>b</em> in Triangle B. Let's say that side <em>h</em> in Triangle A also corresponds with side <em>k</em> 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)

<h2>Solving the Question</h2>

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.

<h2>Answer</h2>

37.5 units

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