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Big Ideas Math: Modeling Real Life, Grade 8

BI

Big Ideas Math: Modeling Real Life, Grade 8 View details

6. The Converse of the Pythagorean Theorem

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Exercise 5 Page 413

The ratio of the corresponding side lengths is equal to the ratio of the perimeters.

4.5

Practice makes perfect

We are given a pair of similar figures.

similar figures

The ratio of the perimeters is 4: 3. Knowing that the ratio of corresponding side lengths is the same as the ratio of the perimeters, we can write a proportion in terms of x. Be sure to keep the larger side length and the larger perimeter on the same side of the fraction bar. 6/x=4/3 Let's isolate x and find its value!

6/x=4/3

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Solve for x

LHS * x=RHS* x

6=4/3(x)

MoveRightFacToNum

a/c* b = a* b/c

6=4x/3

LHS * 3=RHS* 3

6(3)=4x

Multiply

18=4x

.LHS /4.=.RHS /4.

18/4=4x/4

CancelCommonFac

Cancel out common factors

18/4=4x/4

Simplify quotient

18/4=x

Rearrange equation

x=18/4

Calculate quotient

x=4.5

Subchapter links

Try It p.410-411

Self-Assessment for Concepts & Skills p.411-412

Review & Refresh p.413

Concepts, Skills, & Problem Solving p.413-414