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The  length of a rectangle is 2 less than twice its width. The area is 144 squared centimeters. Which quadratic equation in standard form correctly models the situation, where w represents the width of the rectangle

The length of a rectangle is 2 less than twice its width The area is 144 squared centimeters Which quadratic equation in standard form correctly models the situ class=

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masbrosur

Answer:

w² - w - 72 = 0

Step-by-step explanation:

l = 2w - 2

A = 144

A = l * w

A = (2w - 2)w

144 = 2w² - 2w

0 = 2w² - 2w - 144

2w² - 2w - 144 = 0 (divide all by 2)

w² - w - 72 = 0

The quadratic equation which correctly models the situation is,

                                    [tex]w^{2}-w-72=0[/tex]

Let us consider that width is w.

Given that The length of a rectangle is 2 less than twice its width.

     [tex]length=2w-2[/tex]

 Area of rectangle (A) [tex]=length *width[/tex]

The area is 144 squared centimeters.

             [tex]w*(2w-2)=144\\\\2w^{2}-2w-144=0\\\\2(w^{2}-w-72 )=0 \\\\w^{2}-w-72 =0[/tex]                  

Hence, the quadratic equation which correctly models the situation is,

                                    [tex]w^{2}-w-72=0[/tex]

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