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McGraw Hill Glencoe Geometry, 2012

MH

McGraw Hill Glencoe Geometry, 2012 View details

2. The Pythagorean Theorem and Its Converse

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Exercise 45 Page 554

Use the Pythagorean Theorem.

10

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=8, b=x-4, and c=x.

Let's substitute these values into the formula.

a^2+b^2=c^2

SubstituteValues

Substitute values

8^2+( x-4)^2= x^2

▼

Solve for x

ExpandNegPerfectSquare

(a-b)^2=a^2-2ab+b^2

8^2+x^2-2* 4* x + 4^2 = x^2

Calculate power

64+x^2-2* 4* x + 16 = x^2

Multiply

64+x^2-8x+16=x^2

LHS-x^2=RHS-x^2

64-8x+16=0

Add and subtract terms

80-8x=0

LHS+8x=RHS+8x

80=8x

.LHS /8.=.RHS /8.

10=x

Rearrange equation

x=10

Subchapter links

Check Your Understanding p.551-552

Practice and Problem Solving p.552-554

H.O.T. Problems p.554

Standardized Test Practice p.555

Spiral Review p.555

Skills Review p.555