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The expression s^(2) is used to calculate the areag of a square, where s is the side length of the square. What does the expression (8x)^(2) represent?
(A) the area of a square with a side length of 8
(B) the area of a square with a side length of 16
(C) the area of a square with a side length of 4x
(D) the area of a square with a side length of 8x

The expression $s^{2}$ is used to calculate the areag of a square, where $s$ is the side length of the square. What does the expression $(8 x)^{2}$ represent? $\newline$ (A) the area of a square with a side length of $8$ $\newline$ (B) the area of a square with a side length of $16$ $\newline$ (C) the area of a square with a side length of $4 x$ $\newline$ (D) the area of a square with a side length of $8 x$

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Area of quadrilaterals and triangles: word problems

Full solution

Q. The expression

s^{2}

is used to calculate the areag of a square, where

s

is the side length of the square. What does the expression

(8 x)^{2}

represent?

\newline

(A) the area of a square with a side length of

8

\newline

(B) the area of a square with a side length of

16

\newline

(C) the area of a square with a side length of

4 x

\newline

(D) the area of a square with a side length of

8 x

Area Formula for Square: The formula for the area of a square is $s^2$ , where $s$ is the length of one side of the square. In the expression $(8x)^2$ , the term $8x$ is taking the place of $s$ in the area formula. Therefore, $(8x)^2$ represents the area of a square where the side length is $8x$ .
Substitute $8x$ for $s$ : To confirm our understanding, we can expand the expression $(8x)^2$ . This is equivalent to $(8x) \times (8x)$ , which simplifies to $64x^2$ . This confirms that the expression represents the area of a square with each side being $8x$ units long.

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