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Solve for the unknown length.

Solve For The Unknown Length class=

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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?).

  • 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:

[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

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