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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?

Sagot :

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,

[tex]\begin{gathered} N=l^{\prime}w^{\prime} \\ =(9+w)(w+2) \\ =9(w+2)+w(w+2) \\ =9w+9\times2+w^2+2w \\ =11w+18+w^2 \\ =w^2+11w+18 \end{gathered}[/tex]

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

[tex]w^2+11w+18[/tex]

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