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Big Ideas Math Geometry, 2014 View details

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Exercise 3 Page 486

Use the Pythagorean Theorem.

The Value of x: 4sqrt(3)
Do the Side Lengths Form a Pythagorean Triple? No.

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=4, and c=8.

Let's substitute these values into the formula.

a^2+b^2=c^2

SubstituteValues

Substitute values

x^2+ 4^2= 8^2

▼

Solve for x

CalcPow

Calculate power

x^2+16=64

SubEqn

LHS-16=RHS-16

x^2=48

SqrtEqn

sqrt(LHS)=sqrt(RHS)

x=sqrt(48)

SplitIntoFactors

Split into factors

x=sqrt(16*3)

SqrtProd

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

x=sqrt(16)* sqrt(3)

CalcRoot

Calculate root

x=4sqrt(3)

UseCalc

Use a calculator

x = 6.928203...

Since a negative side length does not make sense, we only need to consider positive solutions. Calculating the root, we can see that x is not an integer. Therefore, the side lengths do not form a Pythagorean Triple.

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Exercises p.486

Exercise 3 Page 486

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