Mario is constructing a frame for a 10 in .by 8 in. photo. He wants the frame to be the same width all the way around and the total area of the frame and photo to be 120 square inches. What is the dimension of the frame?

(10+2x)(8+2x) = 120

4x^2 + 36x + 80 = 120
x^2 + 9x + 20 = 30
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x^2 + 9x - 10 = 0
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(x+10)(x-1) = 0
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x = 1 inch
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Ans: Width of frame = 1 in

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raphealnwobi raphealnwobi · Answer 2 · 2021-12-02T12:15:14+01:00

The frame has a width of 1 in so as to create the total area of the frame and photo to be 120 square inches

The photo has dimensions of 10 in .by 8 in.

Let x represent the width of the frame. Therefore:

new length of the photo and frame = 10 + 2x

new width of the photo and frame = 8 + 2x

The area of the photo and frame is:

Area of photo and frame = length * width

(10 + 2x) * (8 + 2x) = 120

80 + 36x + 4x² = 120

4x² + 36x - 40 = 0

x = -10 or x = 1

Since the width cannot be negative, hence, x = 1

The frame has a width of 1 in so as to create the total area of the frame and photo to be 120 square inches

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