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Pearson Geometry Common Core, 2011

PG

Pearson Geometry Common Core, 2011 View details

Chapter Review

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Exercise 4 Page 535

Use the Pythagorean Theorem.

2sqrt(113)

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=14, b=16, and c=x.

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

a^2+b^2=c^2

SubstituteValues

Substitute values

14^2+ 16^2= x^2

▼

Solve for x

Calculate power

196+256=x^2

Add terms

452=x^2

sqrt(LHS)=sqrt(RHS)

sqrt(452)=x

Rearrange equation

x=sqrt(452)

SplitIntoFactors

Split into factors

x=sqrt(4* 113)

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

x=sqrt(4)* sqrt(113)

Calculate root

x=2sqrt(113)

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