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Big Ideas Math Geometry, 2014 View details

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Exercise 1 Page 486

Use the Pythagorean Theorem.

The Value of x: 15
Do the Side Lengths Form a Pythagorean Triple? Yes.

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=12, b=9, and c=x.

Let's substitute these values into the formula.

a^2+b^2=c^2

SubstituteValues

Substitute values

12^2+ 9^2=x^2

▼

Solve for x

CalcPow

Calculate power

144+81=x^2

AddTerms

Add terms

225=x^2

SqrtEqn

sqrt(LHS)=sqrt(RHS)

sqrt(225)=x

RearrangeEqn

Rearrange equation

x=sqrt(225)

CalcRoot

Calculate root

x=15

Since a negative side length does not make sense, we only need to consider positive solutions. Therefore, x=15. We can see that 12, 9, and 15 are all integers and satisfy a^2+b^2=c^2. Therefore, the side lengths form a Pythagorean Triple.

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Exercises p.486

Exercise 1 Page 486

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