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Pearson Geometry Common Core, 2011

PG

Pearson Geometry Common Core, 2011 View details

1. The Pythagorean Theorem and Its Converse

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Exercise 20 Page 496

Use the Pythagorean Theorem.

3sqrt(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=x, b=x, and c=6.

Let's substitute these values into the formula and solve for x.

a^2+b^2=c^2

SubstituteValues

Substitute values

x^2+ x^2= 6^2

▼

Solve for x

Calculate power

x^2+x^2=36

SumToProdTwoTerms

a+a=2a

2x^2=36

.LHS /2.=.RHS /2.

x^2=18

sqrt(LHS)=sqrt(RHS)

x=sqrt(18)

SplitIntoFactors

Split into factors

x=sqrt(9* 2)

sqrt(a* b)=sqrt(a)*sqrt(b)

x=sqrt(9)*sqrt(2)

Calculate root

x=3sqrt(2)

Since a negative side length does not make sense, we only need to consider positive solutions.

Subchapter links

Lesson Check p.495

Practice and Problem-Solving Exercises p.495-498

Standardized Test Prep p.498

Mixed Review p.498