Problem Solving

theachiever wrote:The front of a 6 foot by 8 foot rectangular door has brass rectangular trim.If the trim is as uniformly 1 foot wide,what fraction of the door's front surface is covered by the trim?

A.13/48
B.5/12
C.1/2
D.7/12
E.5/8

Solution:

To solve this problem we can view it as a type of "shaded region" problem, in which we first determine the area of the entire figure and then subtract the area of the unshaded (white) space from the total area to determine the area of the shaded region, which, in this case, is the area of the trim. Let's start with the area of the entire figure. We see from the diagram that the shape is a rectangle 6 feet by 8 feet. Since the area of a rectangle is width x length, we know:

Area = 6 x 8 = 48 sq. ft.

We can determine the area of the trim by first finding the area of the white spaces. We can use a diagram to illustrate this:



We see that, to determine the total area of the two white spaces, we subtract a total of 2 feet from the 6 foot width and 3 feet from the 8 foot length. Thus, the combined area of the two white spaces is:

(6 - 2) x (8 - 3) = 4 x 5 = 20 sq. ft.

Thus, we know that the area of shaded region, i.e., the trim, is:

48 - 20 = 28 sq. ft.

Finally, we can determine the fraction of the door's front surface that is covered by the trim.

Because the area of the trim is 28 sq. ft. and the area of the entire door is 48 sq. ft., the fraction of the door that is covered by the trim is 28/48 = 7/12.

Answer: D