The matematical comprovation of the best size to maximum area

 (Enem - PPL) A school has an empty rectangular plot of land with a perimeter of 40 m, on which it wants to build a single building that takes advantage of as much area as possible.

After an analysis by an engineer, he concluded that, in order to achieve the maximum area of the plot with a single building, the ideal construction would be

A) an 8 m² bathroom.

B) a 16 m² classroom.

C) a 36 m² auditorium.

D) a 100 m² patio.

E) a 160 m² court.

Translated with DeepL.com (free version)

The mathematical comprovation is a graphic so the fórmula is the perimeter is 40m so 2X+2Y=40, X+Y=20; X=20-Y. So you go to that site: https://www.geogebra.org/

and input that formula: Y = X(20-X) and it gonna make that graphic and you gonna look for the apice of the curve that is the maximum that you can have, that gonna be for side X=10, area=100;

For that graphic you can see that for area all the other values for x or y gonna be lower the area.

Rute Bezerra de Menezes Gondim

Ps.:Also this is a 2nd grade you can mathematically find where the curve had his apice without a graphic, had formulas for that. the lower or the higher point in a 2nd grau.