Question

the figure shows a rectangular pool surrounded by a concrete path is x feet(ft) wide on all sides. the pool is 21 ft long and 11 ft wide. the area of the concentrate path is 144ft². what is the value of x? a. 2 b. 4 c. 18 d. 30

Explanation:

Step1: Calculate the area of the outer rectangle

The length of the outer rectangle is \((21 + 2x)\) ft and the width is \((11+ 2x)\) ft. So the area of the outer rectangle \(A_{outer}=(21 + 2x)(11+ 2x)\).
Using the FOIL method:

$$
LATEXBLOCK0
$$

Step2: Calculate the area of the pool

The area of the pool \(A_{pool}=21\times11 = 231\) \(ft^{2}\)

Step3: Calculate the area of the path

The area of the path \(A = A_{outer}-A_{pool}\). Given \(A = 144\) \(ft^{2}\)

$$
LATEXBLOCK1
$$

Using the quadratic formula \(x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\) for \(ax^{2}+bx + c = 0\). Here \(a = 1\), \(b=16\), \(c=-36\)

$$
LATEXBLOCK2
$$

We have two solutions: \(x=\frac{-16 + 20}{2}=2\) and \(x=\frac{-16-20}{2}=-18\). Since \(x>0\) (width can't be negative), we take \(x = 2\)

Answer:

a. 2