McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
Mid-Chapter Quiz
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Exercise 13 Page 661

Notice that the given figure is a 45^(∘)-45^(∘)-90^(∘) triangle.

18

Notice that the given right triangle has a marked angle measuring 45^(∘). Therefore, by the Triangle Angle Sum Theorem the measure of the third angle must also be 45^(∘).

In a 45^(∘)-45^(∘)-90^(∘) triangle, the legs are congruent and the hypotenuse is sqrt(2) times the length of a leg. With this information, we can find the value of each variable. x= sqrt(2) * 9sqrt(2) Finally, we can find the simplest expression for x.
x=sqrt(2) * 9sqrt(2)
x=9sqrt(2)sqrt(2)
x=9(sqrt(2))^2
x=9(2)
x=18