Math CentralQuandaries & Queries


Question from Natalie:

Hi Maths Central,

I am having trouble with quadratic equations. The question is:

Calculate the length 'l' of a rectangular pool by creating and solving a quadratic equation.

1. The rectangular pool is of equal area to a square pool, and a circular pool (5.70m^2).
2. The length of the rectangular pool must be 2m longer than the width 'w'.

Thank you so, so much for your help, Maths Central!

Hi Natalie,

If I understand this correctly your rectangular pool is to have an area of $5.70 m^{2}.$The pools is $l$ meters by $w$ meters and $l$ is 2 meters longer than $w.$ Since the length is $l$ meters the width $w$ must be $l-2$ meters. The area is $l$ times $w$ and hence

\[l \times (l - 2) = 5.70\]

Solve for $l.$

Make sure you check your answer.


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