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Look at the following rectangle.

Find a binomial expression for the width of the rectangle in terms of x. Justify your answer based on the expressions for the rectangle's length and area.


If the width of the rectangle is 21 inches, what is the length and the area? Use appropriate units and explain how you found your answer.​

Look at the following rectangleFind a binomial expression for the width of the rectangle in terms of x Justify your answer based on the expressions for the rect class=

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Answer:

width of rectangle in terms of x =  ( x + 0.5)

Area of rectangle =372

Length of rectangle = 15.5

Step-by-step explanation:

Given that,

Length of rectangle = 2x² + 9x + 4

Area of rectangle = x + 4

To find,

1)

width of rectangle

Formula of area of rectangle

area = length * width

2x² + 9x + 4 = x + 4 * width

2x² + 9x + 4 / ( x + 4) = width

solving the quadratic equation in numerator to find the factors

x = -4 and x = -0.5

( x + 4 )( x + 0.5) / (x + 4) = width

canceling (x + 4) from numerator and denominator

( x + 0.5) = width

So the width of rectangle in terms of x = ( x + 0.5)

2)

suppose width of rectangle = 12

then,

( x + 0.5) = 12

x = 11.5

Area of rectangle = 2x² + 9x + 4

= 2(11.5)² + 9(11.5) + 4

= 372cm

length of rectangle = x + 4

= 11.5 + 4

= 15.5cm

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