Question

A library has 4 square tabletops that measure n inches on each side. The library also has 8 square tabletops that measure 2n inches on each side. The total area of these tabletops is represented by the expression shown below: 4(n)(n) + 8(2n)(2n). Which expression is equivalent to the total area, in square inches, of these tabletops in the library?

a) 4n^2 + 32n^2
b) 12n^2
c) 12n^4
d) 4n^2 + 64n^2

Answer 1

The total area of the tabletops can be represented by the expression 4n^2 + 32n^2, which simplifies to 36n^2. However, due to a potential typo in the provided options, the closest available answer is 4n^2 + 32n^2.

Step-by-step explanation:

The problem involves finding an equivalent expression for the total area of the tabletops in the library. With the formula for the area of a square being side length squared, we can calculate the total area of the tabletops using the expressions provided. The expression for the total area of the four smaller tabletops is 4(n)(n) or 4n^2, and the expression for the total area of the eight larger tabletops is 8(2n)(2n) or 32n^2, after simplifying the given expression.

Adding these two expressions together, we get the equivalent expression 4n^2 + 32n^2. When we combine like terms, this results in 36n^2. However, this final result is not listed in the provided options. It seems there might be a typo in the question. Based on the initial explanation and the calculation we've done, the correct result should indeed be 36n^2, but from the given options, the expression 4n^2 + 32n^2 is the closest one.