Exercise 41 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=176 square units, the length is l = 16 units, and the width is w=x 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 ⇒ 176=( 16)( x) Let's simplify the this equation. We will start by distributing the parentheses on the right-hand side.

176=(16)(x)

RemovePar

Remove parentheses

176=16x

DivEqn

.LHS /16.=.RHS /16.

176/16=16x/16

MovePartNumRight

a* b/c=a/c* b

176/16=16/16* x

CalcQuot

Calculate quotient

11=1* x

IdPropMult

Identity Property of Multiplication

11=x

RearrangeEqn

Rearrange equation

x=11

We found that x is 11 units.

Checking Our Solution

We can check this solution by solving and seeing that the area is 176 square units when the dimensions are multiplied.

A=l * w

SubstituteValues

Substitute values

176? =16* 11

Multiply

Multiply

176=176 ✓