SOLUTION: The following slab of concrete is twice as long as it is wide. The area in which it is placed includes a 1 ft. wide border of 70 square ft. Find the dimensions of the slab.
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Question 82494This question is from textbook Intermediate Algebra
: The following slab of concrete is twice as long as it is wide. The area in which it is placed includes a 1 ft. wide border of 70 square ft. Find the dimensions of the slab. This question is from textbook Intermediate Algebra
You can put this solution on YOUR website! The following slab of concrete is twice as long as it is wide. The area in which it is placed includes a 1 ft. wide border of 70 square ft. Find the dimensions of the slab.
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I assume this is rectangle with a 1 ft path around it which is 70 sq/ft
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Let x = width of the concrete
Then 2x = length of the concrete
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The overall dimensions(including the 1 ft path):
Length = (2x+2)
Width = (x+2)
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(Over all area) - (concrete area) = path area (given as 70 sq/ft)
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(2x+2)*(x+2) - 2x*x = 70
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2x^2 + 6x + 4 - 2x^2 = 70; FOILed (2x+2)(x+2)
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6x + 4 = 70; the 2x^2's cancel
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6x = 70 - 4
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6x = 66
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x = 66/6
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x = 11 ft is the width of the slab; 2*11 = 22 ft is the length
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Check our solution, using the overall dimensions of 24 by 13
(24*13) - (22*11) =
312 - 242 = 70
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Make sense to you? Any questions?
