Question

A poster is to have a total area of 500 square centimeters. There is a margin around the edges of 4 cm at the top and 8 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

A(w) = 692 - 12w - (8000/w)

Explanation:

Since it has a total area of 500 cm², it means that;

A = hw

Where;

A is area

h is height

w is width

Thus;

500 = hw

h = 500/w

We are told that There is a margin around the edges of 4 cm at the top and 8 cm on the bottom and sides where nothing is printed.

Thus;

We have height as; (h - 4 - 8) and width as; (w - 8 - 8)

Thus;

Area = (h - 4 - 8) × (w - 8 - 8)

Area = (h - 12) × (w - 16)

We know that h = 500/w

And we want to find the printed area in terms of the width(w)

Thus;

A(w) = ((500/w) - 12) × (w - 16)

A(w) = 500 - 12w - 8000/w + 192

A(w) = 692 - 12w - (8000/w)

Answer 2

Using the area formula, the appropriate expression for the area of the poster is A(w) = - 8000/w - 12w + 692

Total Area = 500 cm²

Area = Length × width

Entire area can be expressed thus :

• 500 = l × w
• l = 500 / w

Area with print can be expressed thus :

Length with print = (l - 8 - 4) = (l - 12) cm

Height with print = (w - 2(8)) = (w - 16) cm

Area = (l - 12)(w - 16)

Area = (500/w - 12)(w - 16)

Expressing in terms of width :

A(w) = 500 - 8000/w - 12w + 192

A(w) = - 8000/w - 12w + 692

Hence, the required expression is : A(w) = - 8000/w - 12w + 692