Chapter 8.4, Problem 2P

To determine

To find the area of the walkway

Answer to Problem 2P

Area of the walkway = $\left(16x+64\right)$ sq.ft

Explanation of Solution

Given information:

A square outdoor patio is surrounded by a brick way as shown below:

  

Formula Used:

Area of a square of length x unit is $x^2$ sq. Unit

Calculation:

Length of the square shaped outdoor patio = x ft

∴Area of patio = $x^2$ sq.ft

Width of the brick walkway = 4 ft

Total length of patio and walkway = $x+4+4$

  =$x+8$

∴ Total area of patio and walkway = ${\left(x+8\right)}^2$

  =$x^2+2\left(x\right)\left(8\right)+8^2$

  =$x^2+16x+8^2$

Area of walkway = Total area $-$ Area of patio

  =$\left(x^2+16x+8^2\right)-x^2$

  =$\left(x^2-x^2\right)+16x+64$

  =$16x+64$

∴Area of walkway is $\left(16x+64\right)$ sq.ft