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The front of a 6-foot-by-8-foot rectangular door has brass rectangular trim, as indicated by the shading in the...

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The front of a 6-foot-by-8-foot rectangular door has brass rectangular trim, as indicated by the shading in the...

by BTGmoderatorLU » Tue Jan 12, 2021 4:03 pm

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Source: Official Guide
Door.png
The front of a 6-foot-by-8-foot rectangular door has brass rectangular trim, as indicated by the shading in the figure above. If the trim is 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

The OA is D
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Re: The front of a 6-foot-by-8-foot rectangular door has brass rectangular trim, as indicated by the shading in the...

by Scott@TargetTestPrep » Sun Jan 17, 2021 12:34 pm
BTGmoderatorLU wrote: ↑
Tue Jan 12, 2021 4:03 pm
 Source: Official Guide

Door.png

The front of a 6-foot-by-8-foot rectangular door has brass rectangular trim, as indicated by the shading in the figure above. If the trim is 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

The OA is D
Solution:

The area of the front surface of the door is 6 x 8 = 48 sq. ft. The combined area of the two unshaded rectangles is [(6 - 2) x (8 - 3)/2] x 2 = 4 x 5 = 20 sq. ft. Thus the area of the trim (i.e., the shaded region) is 48 - 20 = 28 sq. ft, which is 28/48 = 7/12 of the area of the front surface of the door.

Answer: D

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