SOLUTION: Could you please help me with this word problem?
You are making a square frame of uniform width for a square picture that has side lengths of 2 feet. The total area of the fr
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You are making a square frame of uniform width for a square picture that has side lengths of 2 feet. The total area of the fr
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Question 526024: Could you please help me with this word problem?
You are making a square frame of uniform width for a square picture that has side lengths of 2 feet. The total area of the frame is 5 square feet. What is the length of the sides of the frame?
Kamsahamnida! (Thank You!)
You can put this solution on YOUR website! You are making a square frame of uniform width for a square picture that has side lengths of 2 feet. The total area of the frame is 5 square feet. What is the length of the sides of the frame?
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picture area = 2*2 = 4 sq. ft.
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Let the uniform with of the frame be "x".
The outer dimensions of the frame are (2+2x)ft by (2+2x) ft
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Area of the whole picture with frame = (2+2x)^2 = 4+8x+4x^2
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So, area of the frame alone is 4x^2+8x+4-4 = 4x^2+8x
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Equation:
Solve for "x":
4x^2+8x = 5
4x^2+8x-5 = 0
Positive solution:
x = [-8 + sqrt(64-4*4*-5)]/8
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x = [-8 + sqrt(144)]/8
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x = [-8+12]/8
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x = 1/2 ft
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Length of the out sides of the frame = (2+2x) = 2+1 = 3 ft.
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Cheers,
Stan H.
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