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Sample Question 6:
Step 1: Analyze the problem. The question is asking for the area of the frame which can be found by subtracting the area of the photograph from the total area of the photograph and the frame together.
Step 2: Calculate the area of the photograph using the formula for the area of a rectangle which is \(length \times width\). This gives us \(8 \times 10 = 80\) square inches.
Step 3: Calculate the total height and width of the frame and the photograph together. Here, add the height of the photograph to twice the width of the border to get the total height \(8 + 2 + 2 = 12\) and do the same for the total width \(10 + 2 + 2 = 14\).
Step 4: Use these total dimensions to calculate the total area of the photograph and frame together. This readily gives \(12 \times 14 = 168\) square inches.
Step 5: Ultimately, find the area of the frame by subtracting the area of the photograph from the total area obtained in the previous step. Hence, the area of the frame is \(168 - 80 = 88\) square inches. The answer is \(\boxed{\textbf{(E)}\ 88}\).
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?
\(\textbf{(A)}\hspace{.05in}36\qquad\textbf{(B)}\hspace{.05in}40\qquad\textbf{(C)}\hspace{.05in}64\qquad\textbf{(D)}\hspace{.05in}72\qquad\textbf{(E)}\hspace{.05in}88\)
Answer Keys
Question 6: ESolutions
Question 6Step 1: Analyze the problem. The question is asking for the area of the frame which can be found by subtracting the area of the photograph from the total area of the photograph and the frame together.
Step 2: Calculate the area of the photograph using the formula for the area of a rectangle which is \(length \times width\). This gives us \(8 \times 10 = 80\) square inches.
Step 3: Calculate the total height and width of the frame and the photograph together. Here, add the height of the photograph to twice the width of the border to get the total height \(8 + 2 + 2 = 12\) and do the same for the total width \(10 + 2 + 2 = 14\).
Step 4: Use these total dimensions to calculate the total area of the photograph and frame together. This readily gives \(12 \times 14 = 168\) square inches.
Step 5: Ultimately, find the area of the frame by subtracting the area of the photograph from the total area obtained in the previous step. Hence, the area of the frame is \(168 - 80 = 88\) square inches. The answer is \(\boxed{\textbf{(E)}\ 88}\).