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belka [17]
3 years ago
13

a photograph measures 10 inches by 12 inches. a frame with constant width is placed around the photograph so that the total area

of the framed photo is 288 square inches. what is the width of the frame? enter your answer in the box.
Mathematics
1 answer:
natima [27]3 years ago
7 0
The correct answer is 3 inches.

To find this answer, we need to write and solve a quadratic equation.

Let's call the width of the frame X.

Then, the total width is 10 + 2x and the total length is 12 + 2x.

Having this information, we can write and solve the following equation.

(10 + 2x)(12 + 2x) = 288
4x^2 + 44x + 120 = 288
4x^2 + 44x - 168 = 0
4(x - 3)(x + 14) = 0

The solutions are 3 and -14, but only 3 makes sense in the story problem.
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