Pearson Geometry Common Core, 2011
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Pearson Geometry Common Core, 2011 View details
Mid-Chapter Quiz
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Exercise 2 Page 514

x=10, y=10sqrt(2)

Practice makes perfect
To find the missing side of the triangle, we will use the Pythagorean Theorem. a^2+b^2=c^2

In the formula, a and b are the legs and c is the hypotenuse of a right triangle. We are given a triangle with a=10, b=x, and c=y. Notice that, the legs of our triangle are congruent. Therefore, we immediately have that x=10.

Let's substitute these values into the formula and solve for y.
a^2+b^2=c^2
10^2+ 10^2= y^2
Solve for y
2* 10^2=y^2
sqrt(2* 10^2)=y
y=sqrt(2* 10^2)
y=sqrt(2)* sqrt(10^2)
y=sqrt(2)* 10
y=10sqrt(2)
Since a negative side length does not make sense, we only need to consider positive solutions.