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$A(x) = (8 + 2x)^2$ $\newline$ Carmen wants to add a border around a square picture. The function shows the area of the picture in square inches if it has a border $x$ inches wide. What are the dimensions of the picture without the border?

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Area of quadrilaterals and triangles: word problems

Full solution

Q.

A(x) = (8 + 2x)^2

\newline

Carmen wants to add a border around a square picture. The function shows the area of the picture in square inches if it has a border

x

inches wide. What are the dimensions of the picture without the border?

Find Area Without Border: First, we need to find the area of the picture without the border. Since the function $A(x)$ represents the area with the border, we need to evaluate $A(0)$ because the width of the border is $0$ inches when there is no border.
Calculate Area Without Border: So, $A(0) = (8 + 2\times0)^2 = 8^2 = 64$ square inches.
Find Dimensions of Picture: Now that we have the area of the picture without the border, we can find the dimensions. Since the picture is square, both the length and width are the same.
Calculate Length of Side: To find the length of a side of the square, we take the square root of the area. The square root of $64$ is $8$ inches.

More problems from Area of quadrilaterals and triangles: word problems

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Question

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Question

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\newline

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