   SEARCH HOME Math Central Quandaries & 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.

Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.