Chapter 4.9, Problem 5P

To determine

To calculate:.Find the dimensions of the patio if the area of the garden is $54m^2$ .

Answer to Problem 5P

Width of brick patio is 5 cm and Length of brick patio is 10 cm

Explanation of Solution

Given information: let $w$ be the width of brick, then $2w$ is the length of brick.

Calculation: Then Area of the brick is length*width, i/e.

  $A_B=w*2w=2w^2\mathrm{...}\left(i\right)$

It is bordered on all sides by a garden 1.5 m wide, so its length will be $2w+1.5+1.5=2w+3$ and width will be $w+1.5+1.5=w+3$ , so its area will be

  $A_{B+BORDER}=\left(w+3\right)\left(2w+3\right)$

  $A_{B+BORDER}=2w^2+6w+3w+9$

  $A_{B+BORDER}=2w^2+9w+\mathrm{9...}\left(ii\right)$

area of the garden is $54m^2$ , then

  $54=2w^2+9w+9.-\left(2w^2\right)$

  $54=9w+9$

  $54=9\left(w+1\right)$

  $6=\left(w+1\right)$

  $w=5$

Width of brick patio is 5 cm and Length of brick patio is 2*5 = 10 cm

Conclusion: Width of brick patio is 5 cm and Length of brick patio is 10 cm.