The figure shows ∆ABC ∼ ∆DEF with side lengths as indicated.

What is the value of x?

∆ABC ∼ ∆DEF states that the two triangles are similar.

In similar triangles, the corresponding sides are in proportion. So, set up a proportion to solve for x.

5 in ∆DEF matches up with x in ∆ABC

9 in ∆DEF matches up with 27 in ∆ABC

5 9

--- = ---- {set up a proportion of corresponding sides}

x 27

9x = 135 {cross-multiplied}

In similar triangles, the corresponding sides are in proportion. So, set up a proportion to solve for x.

5 in ∆DEF matches up with x in ∆ABC

9 in ∆DEF matches up with 27 in ∆ABC

5 9

--- = ---- {set up a proportion of corresponding sides}

x 27

9x = 135 {cross-multiplied}

**x = 15**{divided each side by 9}

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