Question

Look at the following rectangle.

Answer 1

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