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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

4. Solving Absolute Value Equations

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Exercise 67 Page 34

The perimeter of a rectangle can be found by adding twice its length $ℓ$ and twice its width $w .$

$9$ cm

Practice makes perfect

We are given a rectangle which has a width of $4$ centimeters and a perimeter of $26$ centimeters. We are asked to find its length.

Because opposite sides in a rectangle are the same length, the perimeter of a rectangle can be found by multiplying its length

ℓ

and width

w

by

2,

then adding those two values.

P = 2 ℓ + 2 w

To find

ℓ,

we can substitute

P = 26

and

w = 4

into the formula, then solve.

P = 2 ℓ + 2 w

$P = 26$ , $w = 4$

26 = 2 ℓ + 2 (4)

Multiply

26 = 2 ℓ + 8

$LHS - 8 = RHS - 8$

18 = 2 ℓ

$LHS / 2 = RHS / 2$

9 = ℓ

Rearrange equation

ℓ = 9

The length of the rectangle is

9

centimeters.

Subchapter links

Communicate Your Answer p.27

Monitoring Progress p.28-31

Exercises p.32-34