Exercise 40 Page 264

To find the value of x and the dimensions of the given rectangle, recall that the area of a rectangle is found by multiplying its length by its width. We see in the diagram that the area is A=45 square units, the length is l = x units, and the width is w=5 units.

Solving for x

We can create an equation to solve for x by substituting the given expressions into the formula for the area of a rectangle. A=l * w ⇒ 45=( x)( 5) Let's simplify the this equation. We will start by distributing the parentheses on the right-hand side.

45=(x)(5)

CommutativePropMult

Commutative Property of Multiplication

45=(5)(x)

RemovePar

Remove parentheses

45=5x

DivEqn

.LHS /5.=.RHS /5.

45/5=5x/5

MovePartNumRight

a* b/c=a/c* b

45/5=5/5* x

CalcQuot

Calculate quotient

9=1* x

IdPropMult

Identity Property of Multiplication

9=x

RearrangeEqn

Rearrange equation

x=9

We found that x is 9 units.

Checking Our Solution

We can check this solution by solving and seeing that the area is 45 square units when the dimensions are multiplied.

A=l * w

SubstituteValues

Substitute values

45? =9* 5

Multiply

Multiply

45=45 ✓