Question

A garden designer designed a square decorative pool. The pool is surrounded by a walkway.On two opposite sides of the pool, the walkway is 8 ft. On the opposite sides, the walkway is 10 ft. The final design for the pool and walkway covers a total area of 1400 square ft.

Answer 1

Note that the pool is in the shape of square with each of its four sides measuring 'x' units.

(a)

So the total length of the rectangular system is given by,

`\begin{gathered} L=x+10+10 \\ L=x+20 \end{gathered}`

Thus, the total length of the rectangle is (x+20) units.

(b)

Similarly the total width of the rectangular system is given by,

`\begin{gathered} W=x+8+8 \\ W=x+16 \end{gathered}`

Thus, the total width of the rectangle is (x+16) units.

(c)

Consider that the area of the rectangular area is calculated as,

`\text{Area}=\text{Length}*\text{ Width}`

Substitute the values,

`\begin{gathered} A=(x+20)(x+16) \\ A=x(x+16)+20(x+16) \\ A=x^2+16x+20x+20*16 \\ A=x^2+36x+320 \end{gathered}`

Thus, the above expression gives the area of the given rectangle.