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,
<h2>1)</h2>
width of rectangle
Formula of area of rectangle
<h3>area = length * width</h3>
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)
<h2> 2)</h2>
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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