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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

2. The Pythagorean Theorem and Its Converse

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Exercise 46 Page 636

Use the Pythagorean Theorem.

15

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-3, b=9. and c=x.

Let's substitute these values into the formula.

a^2+b^2=c^2

SubstituteValues

Substitute values

( x-3)^2+ 9^2= x^2

▼

Solve for x

ExpandNegPerfectSquare

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

x^2-2* 3* x + 3^2 + 9^2 =x^2

Calculate power

x^2-2* 3* x + 9 + 81 =x^2

Multiply

x^2-6x + 9 + 81 =x^2

Add terms

x^2 - 6x + 90 = x^2

LHS-x^2=RHS-x^2

- 6x + 90 = 0

LHS-90=RHS-90

- 6x = - 90

.LHS /(- 6).=.RHS /(- 6).

x = 15

Subchapter links

Exercises p.633-637