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McGraw Hill Integrated II, 2012

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McGraw Hill Integrated II, 2012 View details

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Exercise 8 Page 713

Use the Pythagorean Theorem.

14.1

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=20.

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= 20^2

▼

Solve for x

Calculate power

x^2+x^2=400

Add terms

2x^2=400

.LHS /2.=.RHS /2.

x^2=200

sqrt(LHS)=sqrt(RHS)

x=sqrt(200)

SplitIntoFactors

Split into factors

x=sqrt(100* 2)

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

x=sqrt(100)* sqrt(2)

Calculate root

x=10sqrt(2)

Use a calculator

x=14.14213...

Round to 1 decimal place(s)

x≈ 14.1

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

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