Difference between revisions of "2012 AMC 8 Problems/Problem 6"
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==Problem== | ==Problem== | ||
| − | A rectangular photograph is placed in a frame that forms a border two inches wide on all sides of the photograph. The photograph measures 8 inches high and 10 inches wide. What is the area of the border, in square inches? | + | A rectangular photograph is placed in a frame that forms a border two inches wide on all sides of the photograph. The photograph measures <math>8</math> inches high and <math>10</math> inches wide. What is the area of the border, in square inches? |
| − | <math> \textbf{(A)}\hspace{.05in}36\qquad\textbf{(B)}\hspace{.05in}40\qquad\textbf{(C)}\hspace{.05in}64\qquad\textbf{(D)}\hspace{.05in}72\qquad\textbf{(E)}\hspace{.05in}88 </math> | + | <math>\textbf{(A)}\hspace{.05in}36\qquad\textbf{(B)}\hspace{.05in}40\qquad\textbf{(C)}\hspace{.05in}64\qquad\textbf{(D)}\hspace{.05in}72\qquad\textbf{(E)}\hspace{.05in}88</math> |
==Solution== | ==Solution== | ||
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In order to find the area of the frame, we need to subtract the area of the photograph from the area of the photograph and the frame together. The area of the photograph is <math> 8 \times 10 = 80 </math> square inches. The height of the whole frame (including the photograph) would be <math> 8+2+2 = 12</math>, and the width of the whole frame, <math> 10+2+2 = 14 </math>. Therefore, the area of the whole figure would be <math> 12 \times 14 = 168 </math> square inches. Subtracting the area of the photograph from the area of both the frame and photograph, we find the answer to be <math>168-80 = \boxed{\textbf{(E)}\ 88} </math>. | In order to find the area of the frame, we need to subtract the area of the photograph from the area of the photograph and the frame together. The area of the photograph is <math> 8 \times 10 = 80 </math> square inches. The height of the whole frame (including the photograph) would be <math> 8+2+2 = 12</math>, and the width of the whole frame, <math> 10+2+2 = 14 </math>. Therefore, the area of the whole figure would be <math> 12 \times 14 = 168 </math> square inches. Subtracting the area of the photograph from the area of both the frame and photograph, we find the answer to be <math>168-80 = \boxed{\textbf{(E)}\ 88} </math>. | ||
Revision as of 21:11, 11 February 2020
Problem
A rectangular photograph is placed in a frame that forms a border two inches wide on all sides of the photograph. The photograph measures 
inches high and 
inches wide. What is the area of the border, in square inches?
Solution
In order to find the area of the frame, we need to subtract the area of the photograph from the area of the photograph and the frame together. The area of the photograph is 
square inches. The height of the whole frame (including the photograph) would be 
, and the width of the whole frame, 
. Therefore, the area of the whole figure would be 
square inches. Subtracting the area of the photograph from the area of both the frame and photograph, we find the answer to be 
.
See Also
| 2012 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 5 |
Followed by Problem 7 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
