Question

The area of a rectangle is represented by the polynomial 16x2  56x . The width of the rectangle is given by thebinomial 2x7. (a) Give a monomial expression in terms of x for (b) If the length of the rectangle is 80, what is the the length of the rectangle. Show how you width of the rectangle? Explain your thinking. Arrived at your answer

Answer 1

Answer:

a) Length = $8x$

b) Width = 27 units        

Step-by-step explanation:

We are given the following in the question:

Area of rectangle, A =

$A = 16x^2 + 56x$

Width of rectangle, w =

$w = 2x + 7$

a) Length of the rectangle.

Area of rectangle is given by:

$A = l\times w$

where l is the length of rectangle.

Putting values, we get,

$16x^2 + 56x = a(2x+7)\\\\l = \dfrac{16x^2 + 56x}{2x + 7}\\\\l = \dfrac{8x(2x+7)}{2x+7}=8x$

b) Width of rectangle

Length of rectangle = 80

$8x = 80\\\Rightarrow x = 10$

Thus, width of rectangle is

$2x + 7\\=2(10) + 7= 27$

Thus, the width of rectangle is 27 units.