Questions: Question A photograph with length L and width W is placed on a mat so that there is a border of width 8 cm. The area of the border (in square centimeters, or cm^2) is found to be A=(L+16)(W+16)-L * W. See the figure below. Find the area, in square centimeters, of the border for a photograph with length 32 cm and width 24 cm.

Question
A photograph with length L and width W is placed on a mat so that there is a border of width 8 cm. The area of the border (in square centimeters, or cm^2) is found to be A=(L+16)(W+16)-L * W. See the figure below.

Find the area, in square centimeters, of the border for a photograph with length 32 cm and width 24 cm.
Transcript text: Question A photograph with length $L$ and width $W$ is placed on a mat so that there is a border of width 8 cm . The area of the border (in square centimeters, or $\mathrm{cm}^{2}$ ) is found to be $A=(L+16)(W+16)-L \cdot W$. See the figure below. Find the area, in square centimeters, of the border for a photograph with length 32 cm and width 24 cm .
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Solution

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Solution Steps

Step 1: Calculate the area of the mat

The length of the mat is L + 2 * 8 cm = 32 cm + 16 cm = 48 cm. The width of the mat is W + 2 * 8 cm = 24 cm + 16 cm = 40 cm. The area of the mat is (48 cm)(40 cm) = 1920 cm².

Step 2: Calculate the area of the photograph

The area of the photograph is (32 cm)(24 cm) = 768 cm².

Step 3: Calculate the area of the border

The area of the border is the difference between the area of the mat and the area of the photograph. Area of border = 1920 cm² - 768 cm² = 1152 cm².

Final Answer: The final answer is $\boxed{1152}$

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