Math CentralQuandaries & Queries


Question from Ericka, a student:

You are working as a carpenter in an industrial Shop. A customer came to you and inquired about the size of the table which would be fitted in her room. She informed you that she had already a 1.5 x 1m table in her room but she wanted to maximize the space by adding the same amount to is length and width. She is planning to occupy a 3 square meter place on her room for her to work comfortably. She is requesting you a written recommendation before she asked to make a table. What amount should be added to both sides to maximize a 3 square meter area?

Hi Ericka,

If she adds $x$ meters to each side the table will be $1.5 + x$ meters by $1 + x$ meters and hence its area will be $(1.5 + x)(1 + x)$ square meters. She wants an area of 3 square meters and thus

\[(1.5 + x)(1 + x) = 3.\]

Expanding the left side gives

\[1.5 + 2.5 x + x^2 = 3.\]

I would rather not work with decimals so I am going to write the decimals as improper fractions giving

\[\frac32 + \frac52 x + x^2 = 3.\]

Now multiply both sides by 2 to obtain

\[3 + 5 x + 2 x^2 = 6.\]

Can you solve this for $x?$ Write back if you need more assistance.


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