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The rectangle below has an area of x^2-15x+56 x ​2 ​​ −15x+56 x, start superscript, 2, end superscript, minus, 15, x, plus, 56 square meters and a length of x-7x−7x, minus, 7 meters. what expression represents the width of the rectangle

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meerkat18
By definition, a rectangle is a quadrilateral (4-sided polygon) with two sets of parallel and equal sides called length and width. The area of a rectangle is equal to the product of these two. The equation for the area is a quadratic equation. When you factor out a quadratic equation, it would be a product of two binomials such as (x-q)(x-r) = 0, where q and r are roots or zero's of the equation. You can find this by using the quadratic formula:

[tex]x= \frac{ -b+/- \sqrt{ b^{2}-4ac} }{2a} [/tex]

where a, b and c are the coefficients and constant of the quadratic equation with a general formula of ax²+bx+c=0. Substituting to the equation:

[tex]x= \frac{ -(-15)+/- \sqrt{ (-15)^{2}-4(1)(56)} }{2(1)} [/tex]

x = 7,8

Therefore, the binomials are (x-7) and (x-8). Since it was mentioned that the length is (x-7), then the width is (x-8).

The expression that represents the width of the rectangle is x - 8

Area of a rectangle:

  • area = lw

l = length

w = width

area = x² + 15x + 56

length = x - 7

Therefore,

x² - 15x + 56 = (x - 7) w

divide both sides by x - 7

w = x² - 15x + 56 / x - 7

w = (x - 7)(x - 8) / x - 7

w = x - 8

learn more on rectangle here: https://brainly.com/question/4529723

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