Question 168149
A square mat has a uniform red border on all four sides. The rest of the mat is blue. The width of the blue square is three-fourths the width of the entire square. If the area colored red is 28 m squared, determine the lengths of each side of the mat.
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Let x = length of one side of mat
and y = width of red border
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From: "The width of the blue square is three-fourths the width of the entire square." we get equation 1:
x-2y = (3/4)x
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From:"area colored red is 28 m squared" we get equation 2:
"area of mat" - "area of blue" = "area of red"
x^2 - (x-2y)^2 = 28
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Solve equation 1 for y:
x-2y = (3/4)x
-2y = (3/4)x - x
-2y = -.25x
y = 0.125x
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Substitute the above into equation 2 and solve for x:
x^2 - (x-2y)^2 = 28
x^2 - (x-2(0.125x))^2 = 28
x^2 - (x-.25x)^2 = 28
x^2 - (.75x)^2 = 28
x^2 - 0.5625x^2 = 28
0.4375x^2 = 28
x^2 = 64
x = (+-)8
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Well, we can throw out the negative answer leaving:
x = 8 meters