Question

A poster is to have a total area of 500 square centimeters. There is a margin around the edges of 7 cm at the top and 7 cm on the bottom and sides where nothing is printed. Express the printed area A in terms of the width w (in centimeters) of the bottom.

Answer 1

Answer:

$A_p_r_i_n_t_e_d(w)=5-0.14w$

Explanation:

Take a look at the picture I attached you. The Rectangle area is given by:

$A=w*h$

Where:

$w=width\hspace{3}of\hspace{3}the\hspace{3}rectangle\\h=height\hspace{3}of\hspace{3}the\hspace{3}rectangle$

The total area of the poster is 5m^2, so:

$5=w*h$

Isolating h:

$h=\frac{5}{w}$  (1)

Now, the printed area would be the product between w and h minus the length of the margins, therefore:

$A_p_r_i_n_t_e_d=w*(h-2*0.07)$  (2)

Replacing (1) in (2) and applying distributive property:

$A_p_r_i_n_t_e_d(w)=w*(\frac{5}{w} -0.14)=5-0.14w$