Afarmer wants to build a rectangular pen with 80 feet of fencing. the pen will be built against the wall of the barn so one side of the rectangle won’t need a fence. what dimensions will maximize the area of the pen?

The length of the rectangular pen is

The width of the rectangular pen is

Step-by-step explanation:

Let

x-----> the length of the rectangular pen

y----> the width of the rectangular pen

we know that

The perimeter of the rectangular pen in this problem is equal to

---> remember that one side of the rectangle won’t need a fence

so

-----> equation A

The area of the rectangular pen is equal to

-----> equation B

Substitute equation A in equation B

The quadratic equation is a vertical parabola open downward

The vertex is a maximum

The x-coordinate of the vertex is the length of the rectangular pen that maximize the area of the pen

The y-coordinate of the vertex is the maximum area of the pen

using a graphing tool

The vertex is the point (40,800)

see the attached figure

so

Find the value of y

---->

therefore

The length of the rectangular pen is

The width of the rectangular pen is

step-by-step explanation: the declaration of the rights of man and of the citizen (french: déclaration des droits de l'homme et du citoyen de 1789), set by france's national constituent assembly in 1789, is a human civil rights document from the french revolution.[1]

the declaration was drafted by the abbé sieyès and the marquis de lafayette, in consultation with thomas jefferson.[2] influenced by the doctrine of "natural right", the rights of man are held to be universal: valid at all times and in every place, pertaining to human nature itself. it became the basis for a nation of free individuals protected equally by the law. it is included in the beginning of the constitutions of both the fourth french republic (1946) and fifth republic (1958) and is still current. inspired by the enlightenment philosophers, the declaration was a core statement of the values of the french revolution and had a major impact on the development of freedom and democracy in europe and worldwide.[3]

the 1789 declaration, together with the 1215 magna carta, the 1689 english bill of rights (1689), the 1776 united states declaration of independence, and the 1789 united states bill of rights, inspired in large part the 1948 united nations universal declaration of human rights

ca = ec

cpctc makes it so that corresponding parts of the triangle you proved to be equal are equal, the other options aren't part of the part of the triangles you proved to be equal.