Question

question 2
a swimming pool has a rectangular base with a length of \\( (2x + 3) \\) metres and a width of ... metres.

(a) write and simplify an expression for the perimeter of the pool.

(b) expand and simplify an expression for the area of the pools base.

(c) if the perimeter of the pool is 44 metres, find the value of \\( x \\).

(d) hence state the length and width of the pool.

(e) the pool has a uniform depth of 1.5 metres. find the volume of water the pool can hold, in cubic metres.

Explanation:

Write and simplify perimeter expression

Using the Geometric Formulas knowledge point

$$
LATEXBLOCK0
$$

Expand and simplify area expression

Using the Polynomial Expansion knowledge point

$$
LATEXBLOCK1
$$

Solve for x given perimeter

Using the Geometric Formulas knowledge point

$$
LATEXBLOCK2
$$

Determine length and width

Using the Geometric Formulas knowledge point

$$
LATEXBLOCK3
$$

Calculate pool volume

Using the Geometric Formulas knowledge point

$$
LATEXBLOCK4
$$

Answer:

Question (a)

\(6x + 8\) metres

Question (b)

\(2x^2 + 5x + 3\) square metres

Question (c)

\(x = 6\)

Question (d)

Length is \(15\) metres, width is \(7\) metres.

Question (e)

\(157.5\) cubic metres