Question

special pool order - challenge question!
your client asked for a pool design that has an area of 80 m² and a perimeter of 42 m. based on this information, what are the dimensions of the pool? draw it out and label the measurements in the space below or on the back of your worksheet.

Explanation:

Step1: Define variables for dimensions

Let length = $l$, width = $w$

Step2: Set up area equation

Area: $l \times w = 80$

Step3: Set up perimeter equation

Perimeter: $2(l + w) = 42 \implies l + w = 21$

Step4: Solve the system of equations

From Step3: $l = 21 - w$. Substitute into Step2:
$$(21 - w)w = 80$$
$$w^2 - 21w + 80 = 0$$
Use quadratic formula $w = \frac{21 \pm \sqrt{21^2 - 4 \times 1 \times 80}}{2}$
$$w = \frac{21 \pm \sqrt{441 - 320}}{2} = \frac{21 \pm \sqrt{121}}{2} = \frac{21 \pm 11}{2}$$

Step5: Calculate width values

First solution: $w = \frac{21 + 11}{2} = 16$
Second solution: $w = \frac{21 - 11}{2} = 5$

Step6: Find corresponding lengths

If $w=16$, $l=21-16=5$
If $w=5$, $l=21-5=16$

Answer:

The pool has dimensions of 16 meters and 5 meters (length and width can be swapped).

To draw the pool:

1. Sketch a rectangle.
2. Label one pair of opposite sides as 16 m, and the other pair as 5 m.