A rectangular piece of plastic has an area of 60 square millimeters and a perimeter of 32 millimeters. What are the dimensions of the piece of plastic?

Answer 1

Let x represent the length of the rectangle and y its width.

From the given area write the equation:

xy = 60

From the given perimeter:

2x + 2y = 32, which can be modified to x + y = 16 by dividing every term by 2.

In preparation for using the substitution method solve that last equation for y (for example):

y = 16 -x.

Substitute that expression for y into the equation for area:

x ( 16 - x) = 60.

16x - x²=60

x²-16x+60 = 0

Two numbers that multiply to give 60 and add to -16 are -6 and -10 so the quadratic trinomial factors:

( x - 6) ( x - 10) = 0

Using the zero product property:

x - 6 = 0 OR x -10 = 0, so

x = 6 or x = 10

When x = 6, y =10 (based on one of the original equations).

When x = 10, y = 6.

Since we let x = length we would probably state that the length of the rectangle is 10 and its width is 6.

Check:

Area = LW = 10(6) = 60 square mm.

Perimeter = 2L + 2W = 2(10) + 2(6) = 20 + 12 = 32 mm.