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 56 Page 467

Corresponding sides of similar triangles are proportional.

247 mm or 3 37 mm

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 4 and 11 are corresponding.
  • Similarly, the sides of lengths x and 6+x 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. 4/11=x/6+x We can solve the above proportion to find the value of x. To do so, we will use the Cross Product Property.
4/11=x/6+x
â–Ľ
Solve for x
4(6+x)=11x
24+4x=11x
24=7x
24/7=x
x=24/7
We conclude that the value of x is 247 mm which can be written as a mixed number as 3 37.