Pearson Geometry Common Core, 2011
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Pearson Geometry Common Core, 2011 View details
4. Similarity in Right Triangles
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Exercise 55 Page 467

Corresponding sides of similar triangles are proportional.

9.8 in.

Practice makes perfect

We are told that the triangles are similar, and we want to find the value of x.

Let's identify the two pairs of corresponding sides.
  • The sides of lengths 7+x and 7 are corresponding.
  • Similarly, the sides of lengths 12 and 5 are corresponding.

Also, let's separate these triangles so that it is easier to visualize what we have described above.

Since the two triangles are similar, their corresponding sides are proportional. 7+x/7=12/5 We can solve the above proportion to find the value of x. To do so, we will use the Cross Product Property.
7+x/7=12/5
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Solve for x
(7+x)5=7(12)
35+5x=7(12)
35+5x=84
5x=49
x=9.8
The length of the unknown segment is 9.8 inches.