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zheka24 [161]
2 years ago
8

The unshaded area inside the figure to the right is 648 in.² Use this fact to write an equation involving x. Then solve the equa

tion to find the value of x.
Length of rectangle is 40 inches
Width of rectangle is 22 inches
Border inside rectangle is x
Mathematics
1 answer:
FrozenT [24]2 years ago
3 0

The <em>second order</em> polynomial that involves the variable <em>x</em> (border inside the rectangle) and associated to the <em>unshaded</em> area is x² - 62 · x + 232 = 0.

<h3>How to derive an expression for the area of an unshaded region of a rectangle</h3>

The area of a rectangle (<em>A</em>), in square inches, is equal to the product of its width (<em>w</em>), in inches, and its height (<em>h</em>), in inches. According to the figure, we have two <em>proportional</em> rectangles and we need to derive an expression that describes the value of the <em>unshaded</em> area.

If we know that <em>A =</em> 648 in², <em>w =</em> 22 - x and <em>h =</em> 40 - x, then the expression is derived below:

<em>A = w · h</em>

(22 - x) · (40 - x) = 648

40 · (22 - x) - x · (22 - x) = 648

880 - 40 · x - 22 · x + x² = 648

x² - 62 · x + 232 = 0

The <em>second order</em> polynomial that involves the variable <em>x</em> (border inside the rectangle) and associated to the <em>unshaded</em> area is x² - 62 · x + 232 = 0. \blacksquare

To learn more on polynomials, we kindly invite to check this verified question: brainly.com/question/11536910

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The correct answer is 2.5 cm

Explanation:

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This also means the area of the rectangle is 15 considering both figures have the same area. Additionally, the area in rectangles is calculated by multiplying the length base by the width. This implies in the case presented 6 cm x w cm = 15 cm (total area), and you can determine the value of w by using a simple equation as

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w =  2.5

Also, you can know this is the correct value because 6 cm (length) x 2.5 (width) = 15 cm which is the correct area

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