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Harriet's picture is 8 in x 11 in. She wants the

total area to be 108 in²2. How wide should
the border around the picture be?

1 Answer

2 votes

Explanation:

To find the width of the border, we first need to calculate the area of the picture.

Area of the picture = length x width = 8 in x 11 in = 88 in²

Let the width of the border be "x".

The new length of the picture will be 11+2x, and the new width will be 8+2x.

The total area of the new picture with the border will be:

total area = (11+2x) x (8+2x) = 108 in²

Expanding this equation gives:

88 + 22x + 16x + 4x² = 108

Simplifying and rearranging the terms, we get:

4x² + 38x - 20 = 0

We can solve for x using the quadratic formula:

x = (-b ± sqrt(b² - 4ac)) / 2a

where a = 4, b = 38, and c = -20.

Plugging in these values, we get:

x = (-38 ± sqrt(38² - 4(4)(-20))) / 2(4)

x = (-38 ± sqrt(1936)) / 8

x = (-38 ± 44) / 8

The two possible solutions are:

x = 1.5 or x = -5

Since a negative width for the border does not make sense, the width of the border should be 1.5 inches.

User Marek Stanley
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