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Pearson Geometry Common Core, 2011

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Pearson Geometry Common Core, 2011 View details

Chapter Test

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Exercise 2 Page 537

Use the Pythagorean Theorem.

x=2sqrt(14)

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=13, b=x, and c=15.

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

a^2+b^2=c^2

SubstituteValues

Substitute values

13^2+ x^2= 15^2

▼

Solve for x

Calculate power

169+x^2=225

LHS-169=RHS-169

x^2=56

sqrt(LHS)=sqrt(RHS)

x=sqrt(56)

SplitIntoFactors

Split into factors

x=sqrt(4* 14)

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

x=sqrt(4)* sqrt(14)

Calculate root

x=2sqrt(14)

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