Chapter 14.4, Problem 29PPS

a.

To determine

Towrite:the expression in the simplest form and for the area of pattern if each rectangle is $y+5\text{units}$ long and $y\text{units}$ wide.

Answer to Problem 29PPS

  $7y^2+35y$ .

Explanation of Solution

Given:

Thepattern of Jumby game plays on Caribbean island is shown below:

  

Calculation:

According to thequestion, the lengthis $y+5\text{units}$ and width is $y\text{units}$ ,

Therefore, area of each rectangle is

  $\begin{array}{l}A=l\times w\\ =\left(y+5\right)y\\ \left\{by\text{distributive property}\right\}\\ =\left(y^2+5y\right)\end{array}$

Now, area of pattern is 7 times the area of each rectangle.

Therefore,

  $\begin{array}{l}A=7\left(areaofeachrectangle\right)\\ =7\left(y^2+5y\right)\\ A=l\times w\\ \left\{by\text{distributive property}\right\}\\ =7y^2+35y\end{array}$ .

Hence, the expression of area of the given pattern is $7y^2+35y$ .

b.

To determine

To find: the area of pattern if width is known.

Answer to Problem 29PPS

  $1050\text{unit}$ .

Explanation of Solution

Given:

  $y=10\text{unit}$

Calculation:

From part (a), the area of the given pattern is $7y^2+35y$ .

It is given that width is 10units.

Therefore, area of given pattern is

  $\begin{array}{l}A=7{\left(10\right)}^2+35\left(10\right)\\ =700+350\left\{\text{simplify}\right\}\\ =1050\text{unit}\end{array}$ .

Hence, the area of the given pattern is $1050\text{unit}$ .