Question

The floor of a rectangular cage has a length 7 feet greater than its width, w. Elena will increase both dimensions of the floor by 2 feet. Which equation represents the new area, N, of the floor of the cage?

Answer 1

Given:

The length of the floor is 7 feet greater than its width w.

Therefore, length, l=7+w.

Since the dimensions are increased by 2 feet,

The new width, w'=w+2.

The new length, l'=l+2=7+w+2=9+w.

Now, the new area N of the floor of the rectangular cage is,

`\begin{gathered} N=l^(\prime)w^(\prime) \\ =(9+w)(w+2) \\ =9(w+2)+w(w+2) \\ =9w+9*2+w^2+2w \\ =11w+18+w^2 \\ =w^2+11w+18 \end{gathered}`

Therefore, the new area of the floor of the rectangular cage is,

`w^2+11w+18`