Hello!
The problem has given us a garden that measures 12 meters by 14 meters. She wants to increase the total area by increasing the length and width by the same amount. These two phrases (bold) can be used to find the correct equation.
Holly wants to increase the length of the two sides. Therefore, we can eliminate the following two equations:
255 = (12)(14)
255 = (12 – x)(14 – x)
The first equation does not increase either side, but rather keeps both sides at their original length. The second equation decreases the measure of both sides. Holly has also said that she wants to increase both sides by “the same amount.” Therfore, we can also eliminate the following equation:
255 = (12 + [tex] x^{2} [/tex])(14)
This equation only increases the measure of one side. There is now only one equation remaining:
255 = (12 + x)(14 + x)
This equation increases both sides of the garden by the same amount. Therfore, we can conclude that the correct equation is 255 = (12 + x)(14 + x).
I hope this helps!
